44 


ELEMENTARY    LESSONS   IN   LOGIC 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON   •    CHICAGO 
SAN    FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON  •    BOMBAY   •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTE 

TORONTO 


ELEMENTARY    LESSONS 
IN  LOGIC: 

DEDUCTIVE  AND   INDUCTIVE, 
WITH  COPIOUS  QUESTIONS  AND  EXAMPLES 

AMD 

A  VOCABULARY  OF  LOGICAL  TERMS. 


W.   STANLEY   JEVONS,   M.A. 

PROFESSOR    OF   LOGIC    IN   OWENS    COLLEGE,    MANCHKSTBm 

NE  W  EDITION. 


THE   MACMILLAN   COMPANY 
1918 

All  rights  reserved 


PREFACE. 

IN  preparing  these  Lessons  I  have  attempted  to 
show  that  Logic,  even  in  its  traditional  form,  can  be 
made  a  highly  useful  subject  of  study,  and  a  powerful 
means  of  mental  exercise.  With  this  view  I  have 
avoided  the  use  of  superfluous  technical  terms,  and 
have  abstained  from  entering  into  questions  of  a 
purely  speculative  or  metaphysical  character.  For 
the  puerile  illustrations  too  often  found  in  works  on 
Logic  I  have  generally  substituted  examples  drawn 
from  the  distinct  objects  and  ideas  treated  in  the 
natural  and  experimental  sciences;  and  in  this  and 
other  respects  have  aimed  at  rendering  these  Lessons 
a  suitable  companion  to  a  series  of  science  school 
books. 


2033685 


PREFACE. 

Logic  is  not  only  an  exact  science,  but  is  the 
t  simple  and  elementary  of  all  sciences ;  it  ought 
therefore  undoubtedly  to  find  some  place  in  every 
course  of  education.  The  relations  of  propositions 
and  the  forms  of  argument  present  as  precise  a  sub- 
ject of  instruction  and  as  vigorous  an  exercise  of 
thought,  as  the  properties  of  geometrical  figures,  or 
the  rules  of  Algebra.  Yet  every  school-boy  is  made 
to  learn  mathematical  problems  which  he  will  never 
employ  in  after  life,  and  is  left  in  total  ignorance  of 
those  simple  principles  and  forms  of  reasoning  which 
will  enter  into  the  thoughts  of  every  hour.  Logic 
should  no  longer  be  considered  an  elegant  and  learn- 
ed accomplishment;  it  should  take  its  place  as  an 
indispensable  study  for  every  well-informed  person. 
These  Lessons  I  trust  will  introduce  to  the  science 
many  who  have  not  leisure  or  inclination  to  read  more 
elaborate  treatises,  and  many  who  would  not  be  at- 
tracted by  the  numerous  but  somewhat  dry  and  brief 
compendiums  published  in  past  years, 

It  is  desirable  that  Lessons  in  Logic  should  be 
made  the  basis  of  many  exercises,  and  for  this  pur- 
pose I  have  supplied  abundance  of  questions  and 
examples  at  the  end  of  the  book,  some  of  which  an 
selected  from  the  examination  papers  of  the  Oxford, 


PREFACE.  Y* 

London,  and  Edinburgh  Universities.  In  my  owt 
classes  I  have  constantly  found  that  the  working  and 
solution  of  logical  questions,  the  examination  of  argu- 
ments and  the  detection  of  fallacies,  is  a  not  lew 
practicable  and  useful  exercise  of  mind  than  is  the 
performance  of  calculations,  and  the  solution  of  pro- 
blems in  a  mathematical  class. 

Except  in  a  few  places,  where  special  notice  is 
given,  I  hare  abstained  from  putting  forward  any 
views  not  commonly  accepted  by  teachers  of  logic; 
and  I  have  throughout  devoted  more  attention  to 
describing  clearly  and  simply  the  doctrines  in  which 
logicians  generally  agree,  than  discussing  the  points 
in  which  there  is  a  difference  of  opinion.  The  recent 
logical  discoveries  of  Sir  W.  Hamilton,  Archbishop 
Thomson,  Prof,  de  Morgan,  and  especially  the  late 
ProC  Boole,  cannot  yet  be  fully  adopted  in  an  ele- 
mentary work,  but  I  have  attempted  to  give  a  clear 
notion  of  the  results  to  which  they  inevitably  lead. 

In  the  latter  Lessons  which  treat  of  Induction  I 
have  generally  followed  Sir  John  Herschel,  Dr  Whewell 
and  Mr  J.  S.  Mill,  as  the  recognised  authorities  on  the 
subject  These  Lessons  in  fact  may  be  regarded  as 
an  easy  introduction  to  some  of  the  most  important 
parts  of  Mr  Mill's  treatise  on  Logic 


viii  PREFACE. 

At  the  end  of  almost  every  Lesson  will  be  found 
references  to  the  works  in  which  the  student  will  most 
profitably  continue  ms  reading  of  the  subject  treated, 
so  that  this  little  volume  may  serve  as  a  guide  tc  1 
•lore  extended  course  of  study. 


TABLE   OF   CONTENTS. 


L        DEFINITION  and  Sphere  of  the  Sdeoot    .........  I 

IL        The  Three  Parts  of  Logical  Doctria*    ............  9 

TERMS. 

III.  Terms,  and  their  various  Kinds  „....  16 

IV.  Of  the  Ambiguity  of  Termi..... ^ 17 

V.        Of  the  twofold  meaning  of  term*— in  Extension 

and  Intension    ...»„. »*,.. .................... ........  *7 

VL       The  Growth  of  Language .. .^.. 44 

VIL      Leibnitz  on  Knowledge _.........._..»._...  ff 

PROPOSITIONS. 

V1IL      Kinds  of  Proposition* « ..............  60 

IX.       The  Opposition  of  Proposition* „ 71 

X.        Conversion  of  Propositions,  and  Immediate  In- 
ference   « .•  8* 

XL       Logical  Analysis  of  Sentences -  88 

X1L      The  Predicates,  Division,  and  Definitiom 9! 

XIII.      Pascal  and  Descartes  on  Method Iff 


TABLE  OF  CONTENTS. 


SYLLOGISM. 


XIV. 
XV. 

XVL 
XVIL 
XVIIL 
XIX, 


XX. 
XXI. 


The  Laws  of  Thought  

The  Rules  of  the  Syllogism 

The  Moods  and  Figures  of  the  Syllogism. 

Reduction  of  the  Imperfect  Figures    

Irregular  and  Compound  Syllogism*  .~v.. 
Of  Conditional  Arguments.. ............. 


FALLACIES. 


Logical  Fallacies... 
Material  Fallacies 


...  15* 

...  i6o 


—  169 


RECENT  LOGICAL  VIEWS. 

XXII.  The  Quantification  of  the  Predicate    ............  i»J 

XXIII.  Book's  System  of  Logic    __......  If 

METHOD. 

XXIV.  Of  Method,  Analysis,  and  Synthesis  „___  «O! 


INDUCTION. 


XXV. 

XXVI. 


Perfect  Induction  and  the  Inductive  Syllogism  sic 
Geometrical  and  Mathematical  Induction,  Ana- 

logy, and  Example   ........  „  ....................  »j8 

XXVIL     Observation  and  Experiment  ..........  ,  .........  —  118 

tXVUL    Methods  of  Induction  ..........  „  .....................  130 

XXIX.      Methods  of  Quantitative  Induction  __________  »47 


TABLE  OF  CONTENTS. 


XXX.       Empirical  and  Deductive  Methods    *5g 

XXXI,  Explanation,    Tendency,    Hypothesis,    Theory 

and  Fact „.  *6* 

SUBSIDIARIES  OF  INDUCTION. 

XXXII.  Classification,  and  Abstraction    376 

Jf  'XIII.    Requisites  of  a  Philosophical  Language 087 


Questions  and  Exercises 496 

Examples  of  Terms  ........  197—^99 

Examples  of  Propositions  - 303 

Examples  of  Arguments    ~  $i»,  315 

...........................0. ...%....«.».....-.  331 


INTRODUCTION. 
LESSON  I. 

DEFINITION  AND  SPHERE  OF  THE  SCIENCE 

LOGIC  may  be  most  briefly  defined  as  the  Science  ol 
Reasoning.  It  is  more  commonly  defined,  however,  as  the 
Science  of  the  Laws  of  Thought,  and  some  logicians  think 
it  desirable  to  specify  still  more  accurately  that  it  is  the 
Science  of  the  Formal,  or  of  the  Necessary  Laws  of 
Thought.  Before  these  definitions  can  be  of  any  real 
use  to  us  we  must  come  to  a  clear  understanding  as  to 
the  meaning  of  the  expressions;  and  ft  will  probably 
appear  that  there  is  no  great  difference  between  them. 

By  a  Law  of  Thought  we  mean  a  certain  uniformity  or 
agreement  which  exists  and  must  exist  in  the  modes  in 
which  all  persons  think  and  reason,  so  long  as  they  do  n&t 
make  what  we  call  mistakes,  or  fall  into  self-contradiction 
and  fallacy.  The  laws  of  thought  are  natural  laws  with 
which  we  have  no  power  to  interfere,  and  which  are  of 
course  not  to  be  in  any  way  confused  with  the  artificial  laws 
of  a  country,  which  are  invented  by  men  and  can  be  altered 
by  them.  Every  science  is  occupied  in  detecting  and 
describing  the  natural  laws  which  are  inflexibly  observed 


•  DEFINITION  AND  SPHERE         [LESS 

by  the  objects  treated  in  the  Science.  'Ine  science  pi 
astronomy  investigates  the  uniform  or  similar  way  in 
which  the  heavenly  bodies,  and  in  fact  all  material  sub- 
stances, tend  to  fall  towards  each  other  as  a  stone  falls 
towards  the  earth,  or  to  move  round  each  other  under 
the  influence  of  this  tendency.  The  universal  law  of 
gravitation  is  thus  the  natural  law  or  uniformity  treatec 
in  physical  astronomy. 

In  chemistry  the  law  of  equivalent  proportions  de- 
»cribes  the  well  ascertained  fact  that  each  chemical 
substance  enters  into  combination  with  every  other  che- 
mical substance  only  in  certain  definite  proportions ;  as 
when  exactly  eight  parts  by  weight  of  oxygen  unite  with 
one  part  of  hydrogen  to  form  water,  or  sixteen  parts  of 
oxygen  and  six  parts  of  carbon  unite  to  form  carbonic 
acid  in  the  ordinary  burning  of  a  flame  or  fire.  When- 
ever we  can  detect  uniformities  or  similarities  we  so  far 
create  science  and  amve  at  natural  laws.  But  there  may 
be,  and  are,  many  things  so  fickle,  complicated,  and 
uncertain,  that  we  can  never  be  sure  we  have  detected 
laws  that  they  will  uniformly  obey ;  in  such  cases  no 
science,  in  the  proper  sense  of  the  word,  is  possible. 
There  is  no  such  thing,  for  instance,  as  a  real  science  of 
human  character,  because  the  human  mind  is  too  variable 
and  complicated  a  subject  of  investigation.  There  are 
no  two  persons  so  much  alike  that  you  may  be  sure  of 
one  acting  in  all  circumstances  as  the  other  would;  it 
thus  becomes  impossible  to  arrange  persons  in  classes  so 
that  all  who  are  in  the  same  class  shall  act  uniformly  in 
the  same  manner  in  any  given  circumstances. 

But  there  is  a  science  of  human  reason  or  thought 
apart  from  the  many  other  acts  of  mind  which  belong  to 
human  character,  because  there  are  modes  in  which  all 
persons  do  uniformly  think  and  reason,  and  must  think 
**»H  reason.  Thus  if  two  things  are  identical  with  a  third 


Ll  OF  THE  SCIENCE.  3 

common  thing  they  are  identical  with  each  othei.  Thit 
is  a  law  of  thought  of  a  very  simple  and  obvious  charac- 
ter, and  we  may  observe  concerning  it, — 

1.  That  all  people  think  in  accordance  with  it,  and 
agree  that  they  do  so  as  soon  as  they  understand  iti 
meaning. 

2.  That  they  think  in  accordance  with  it  whatever 
may  be  the  subject  about  which  they  are  thinking. 

Thus  if  the  things  considered  arc — 

London, 

The  Metropolis, 

The  most  populous  city  in  Great  Britain, 
since  "the  Metropolis  is  identical  with  London,"  and 
"London  is  identical  with  the  most  populous  city  in 
Great  Britain,"  it  follows  necessarily  in  all  minds  that 
"  the  metropolis  is  identical  with  the  most  populous  city 
in  Great  Britain." 

Again,  if  we  compare  the  three  following  things— 

Iron, 

The  most  useful  metal, 

The  cheapest  metal, — 

and  it  be  allowed  that  "  The  most  useful  metal  is  Iron," 
and  "  Iron  is  the  cheapest  metal,*  it  follows  necessarily 
in  all  minds  that  "the  most  useful  metal  is  the  cheapest" 
We  here  have  two  examples  of  the  general  truth  that 
things  identical  with  the  same  thing  are  identical  with 
each  other ;  and  this  we  may  say  is  a  general  or  necessary 
form  of  thought  and  reasoning. 

Compare,  again,  the  following  three  things, — 

The  earth, 

Planets, 

Bodies  revolving  in  elliptic  orbits. 

We  cannot  say,  as  before,  that  "the  earth  is  identical 
-fch  the  planets;"  it  is  identical  only  with  one  of  the 

1—2 


«  DEFINITION  AND  SPHERE        [LES& 

planets,  and  we  therefore  say  that  "  it  is  a  planet"  Sim* 
Arly  we  may  say  that  "  the  planets  are  bodies  revolving 
in  elliptic  orbits,"  but  only  a  part  of  the  whole  number 
so  revolving.  Nevertheless  it  follows  that  if  the  earth  is 
among  the  planets,  and  the  planets  among  bodies  re- 
volving in  elliptic  orbits,  then  the  earth  is  among  the 
latter. 

A  very  elementary  knowledge  of  chemistry  enables  «s 
to  argue  similarly  concerning  the  following  ;— 

Iron, 

Metals, 

Elementary  substances. 

Iron  is  one  of  the  metals,  and  metals  are  elements  ot 
simple  undecomposable  substances,  in  the  sense  of  being 
among  them  or  a  part  of  them,  but  not  as  composing  the 
whole.  It  follows  necessarily  that  "  Iron  is  one  of  the 
elementary  substances."  We  have  had  then  two  exam- 
ples of  a  fixed  and  necessary  form  of  thought  which  is 
necessary  and  true  whatever  the  things  may  be  to  which 
it  is  applied  The  form  of  argument  may  be  expressed  in 
several  different  ways,  and  we  shall  have  to  consider  k 
minutely  in  the  lessons  on  the  syllogism ;  we  may  express 
it,  for  instance,  by  saying  that  "part  of  a  part  is  part 
of  the  whole."  Iron  is  part  of  the  class  of  metals,  which 
is  part  of  the  class  of  elements:  hence  iron  is  part  of 
the  class  of  elements. 

If  I  now  introduce  another  definition  of  Logic  and 
say  that  it  is  "the  science  of  the  necessary  forms  of 
thought,"  the  reader  will  I  hope  clearl)  apprehend  the 
meaning  of  the  expression  "  necessary  forms  of  thought." 
A  fora  is  something  which  may  remain  uniform  and 
unaltered,  while  the  matter  thrown  into  that  torm  may  be 
raried.  Medals  struck  from  the  same  dies  have  exactly 
the  same  form,  but  they  may  be  of  various  matter,  as 


j.]  OF  THE  SCIENCE.  S 

bronze,  copper,  gold  or  silver.  A  building  of  exactly  the 
same  form  might  be  constructed  either  of  stone  or  bricks  ; 
furniture  of  exactly  similar  shape  may  be  made  of  oak, 
mahogany,  walnut  wood,  etc.  Just  as  we  thus  familiarly 
recognize  the  difference  of  form  and  substance  in  common 
tangible  things,  so  we  may  observe  in  Logic,  that  the 
form  of  an  argument  is  one  thing,  quite  distinct  from  the 
various  subjects  or  matter  which  may  be  treated  in  that 
form.  We  may  almost  exhibit  to  the  eye  the  form  of 
reasoning  to  which  belong  our  two  latter  arguments,  af 
follows:— 


(X)  ......  is  .....  .(Z) 

If  within  the  three  pairs  of  brackets,  marked  respect- 
ively X,  Y  and  Z  we  place  three  names,  such  that  the 
one  in  place  of  X  may  be  said  to  come  under  that  in  Yt 
and  that  in  Y  under  that  in  Z,  then  it  necessarily  follows 
that  the  first  (X)  comes  under  the  last  (Z). 

Logic,  then,  is  the  science  occupied  in  ascertaining 
and  describing  all  the  general  forms  of  thought  which  we 
must  employ  so  long  as  we  reason  validly.  These  forms 
are  very  numerous,  although  the  principles  on  which  they 
are  constructed  are  few  and  simple.  It  will  hence  appear 
that  logic  is  the  most  general  of  all  the  sciences.  Its 
aid  must  be  more  often  required  than  the  aid  of  any  other 
science,  because  all  the  particular  sciences  treat  portions 
only  of  existing  things,  and  create  very  different  and 
often  unconnected  branches  of  knowledge.  But  logic 
treats  of  those  principles  and  forms  of  thought  which 
must  be  employed  in  every  branch  of  knowledge.  It 
treats  of  the  very  origin  and  foundations  of  knowledge 
itself;  and  though  it  is  true  that  the  logical  method  em- 
ployed in  one  science  may  differ  somewhat  from  that  era- 


6  DEFINITION  AND  SPHERE 

ployed  in  another  science,  yet  whatever  the  particulai 
form  may  be,  it  must  be  logical,  and  must  conform  to  thi 
laws  of  thought.  There  is  in  short  something  in  which 
all  sciences  must  be  similar;  to  which  they  must  con- 
form so  long  as  they  maintain  what  is  true  and  self* 
consistent;  and  the  work  of  logic  is  to  explain  this 
common  basis  of  all  science. 

One  name  which  has  been  given  to  Logic,  namely  the 
Science  of  Sciences,  very  aptly  describes  the  all  extensive 
power  of  logical  principles.  The  cultivators  of  special 
branches  of  knowledge  appear  to  have  been  fully  aware 
of  the  allegiance  they  owe  to  the  highest  of  the  sciences. 
for  they  have  usually  given  names  implying  this  allegi- 
ance. The  very  name  of  logic  occurs  as  part  of  nearly 
all  the  names  recently  adopted  for  the  sciences,  which  are 
often  vulgarly  called  the  "ologies,"  but  are  really  the 
"logics,"  the  "o"  being  only  a  connecting  vowel  or  part 
of  the  previous  word.  Thus  geology  is  logic  applied  to 
explain  the  formation  of  the  earth's  crust ;  biology  is  logic 
applied  to  the  phenomena  of  life ;  psychology  is  logic 
applied  to  the  nature  of  the  mind ;  and  the  same  is  the 
case  with  physiology,  entomology,  zoology,  teratology, 
morphology,  anthropology,  theology,  ecclesiology,  thalat- 
tology,  and  the  rest*.  Each  science  is  thus  distinctly 
confessed  to  be  a  special  logic.  The  name  of  logic  itself 
is  derived  from  the  common  Greek  word  \oyos,  which 
usually  means  word,  or  the  sign  and  outward  manifesta- 
tion of  any  inward  thought.  But  the  same  word  was  also 
used  to  denote  the  inward  thought  or  reasoning  of  which 
words  are  the  expression,  and  it  is  thus  probably  that  latei 
Greek  writers  on  reasoning  were  led  to  call  their  science 

•  Except  Philology,  which  is  differently  formed,  and  meaai 
the  love  or  stud*  of  words ;  the  name  of  this  •ritnCT.  if  formed 
opoa  the  same  plan,  would  be  logology. 


L)  OP  THE  SCIENCE. 


oj,  or  logical  science  ;  also  rtynf  Aoyuof,  ot 
logical  art.  The  adjective  XoytKij,  being  used  alone,  sooa 
came  to  be  the  name  of  the  science,  just  as  Mathematic, 
Rhetoric,  and  other  names  ending  in  "ic"  were  ori- 
ginally adjectives  but  have  been  converted  into  substan- 
tives. 

Much  discussion  of  a  somewhat  trifling  character  has 
arisen  upon  the  question  whether  Logic  should  be  con- 
sidered a  science  only,  an  art  only,  or  both  at  the  same 
time.  Sir  W.  Hamilton  has  even  taken  the  trouble  to 
classify  almost  all  the  writers  on  logic  according  as  they 
held  one  opinion  or  the  other.  But  it  seems  substan- 
tially correct  and  sufficient  to  say,  that  logic  is  a  science 
in  so  far  as  it  merely  investigates  the  necessary  princi- 
ples and  forms  of  thought,  and  thus  teaches  us  to  under- 
stand in  what  correct  thinking  consists;  but  that  it  be- 
comes an  art  when  it  is  occupied  in  framing  rules  to  assist 
persons  in  detecting  false  reasoning.  A  science  ttachM  ua 
to  know  and  an  art  to  do,  and  all  the  more  perfect  sciences 
lead  to  the  creation  of  corresponding  useful  arts.  As- 
tronomy is  the  foundation  of  the  art  of  navigation  on  the 
ocean,  as  well  as  of  the  arrangement  of  the  calendar  and 
chronology.  Physiology  is  the  basis  of  the  art  of  medi- 
cine, and  chemistry  is  the  basis  of  many  useful  arts. 
Logic  has  similarly  been  considered  as  the  basis  of  an  art 
of  correct  reasoning  or  investigation  which  should  teach 
the  true  method  to  be  observed  in  all  sciences.  The  cele- 
brated British  logician  Duns  Scotus,  who  lived  in  the  I3th 
century,  and  called  logic  the  Science  of  Sciences,  called  it 
also  the  Art  of  Arts,  expressing  fully  its  preeminence. 
Others  have  thus  defined  it—"  Logic  is  the  art  of  direct- 
ing the  reason  aright  in  acquiring  the  knowledge  o( 
things,  for  the  instruction  both  of  ourselves  and  others," 
Dr  Isaac  Watts,  adopting  this  view  of  logic,  called  hit 
well-known  work  "  the  Art  of  Thinking." 


8  DEFINITION  AND  SPHERE         LLEa 

It  may  be  fairly  said  however  that  Logic  has  mort 
the  form  of  a  science  than  an  art  for  this  reason — all 
persons  necessarily  acquire  the  faculty  and  habit  of  rea- 
soning long  before  they  even  know  the  name  of  logic. 
This  they  do  by  the  natural  exertion  of  the  powers  of 
mind,  or  by  constant  but  unconscious  imitation  of  others. 
They  thus  observe  correctly  but  unconsciously  the  prin- 
ciples of  the  science  in  all  very  simple  cases ;  but  the  con- 
tradictory opinions  and  absurd  fallacies  which  are  put 
forth  by  uneducated  persons  shew  that  this  unaided  ex- 
ercise of  mind  is  not  to  be  trusted  when  the  subject  of 
discussion  presents  any  difficulty  or  complexity.  The 
study  of  logic  then  cannot  be  useless.  It  not  only 
explains  the  principles  on  which  every  one  has  often 
reasoned  correctly  before,  but  points  out  the  dangers 
which  exist  of  erroneous  argument.  The  reasoner  thus 
becomes  consciously  a  correct  reasoner  and  learns  con- 
sciously to  avoid  the  snares  of  fallacy.  To  say  that 
men  can  reason  well  without  logical  science  is  about  as 
true  as  to  say  that  they  can  live  healthily  without  medi- 
cine. So  they  can — as  long  as  they  are  healthy ;  and  so 
can  reasoners  do  without  the  science  of  reasoning — as  long 
as  they  do  reason  correctly ;  but  how  many  are  there  that 
can  do  so  ?  As  well  might  a  man  claim  to  be  immortal 
in  his  body  as  infallible  in  his  mind. 

And  if  it  be  requisite  to  say  a  few  words  in  defence  of 
Logic  as  an  art,  because  circumstances  in  the  past  his- 
tory of  the  science  have  given  rise  to  misapprehension, 
can  it  be  necessary  to  say  anything  in  its  praise  as  a 
science  ?  Whatever  there  is  that  is  great  in  science  or  in 
art  or  in  literature,  it  is  the  work  of  intellect  In  bodily 
form  man  is  kindred  with  the  brutes,  and  in  his  perish- 
able  part  he  is  but  matter.  It  is  the  possession  of  con- 
scious intellect,  the  power  of  reasoning  by  general  notions 
that  raises  him  above  all  else  upon  the  earth ;  and  wh« 


IL]  OF  THE  SCIENCE.  \ 

can  say  that  the  nature  and  procedure  of  this  intellect  if 
not  almost  the  highest  and  most  interesting  subject  of 
study  in  which  we  can  engage?  In  vain  would  an? 
one  deny  the  truth  of  the  favourite  aphorism  of  Sir  W 
Hamilton— 

IN  THE  WORLD  THERE  IS  NOTHING  GREAT  BUT  1CAM 
IN  MAN  THERE  IS  NOTHING  GREAT  BUT  MIND. 


LESSON   II. 
THE  THREE  PARTS  OF  LOGICAL  DOCTRINE. 

IT  has  been  explained  in  the  previous  lesson  that  Logic 
is  the  Science  of  Reasoning,  or  the  Science  of  those  Ne- 
cessary Laws  of  Thought  which  must  be  observed  if  we 
are  to  argue  consistently  with  ourselves  and  avoid  self- 
contradiction.  Argument  or  reasoning  therefore  is  the 
strictly  proper  subject  before  us.  But  the  most  conve- 
nient and  usual  mode  of  studying  logic  is  to  consider  first 
the  component  parts  of  which  any  argument  must  be 
made  up.  Just  as  an  architect  must  be  acquainted  with 
the  materials  of  a  building,  or  a  mechanic  with  the  ma* 
terials  of  a  machine,  before  he  can  pretend  to  be  ac- 
quainted with  its  construction,  so  the  materials  and  in- 
struments with  which  we  must  operate  in  reasoning  arc 
suitably  described  before  we  proceed  to  the  actual  forms 
of  argument 

If  we  examine  a  simple  argument  such  as  that  giret 
in  the  last  lesson,  thus — 

Iron  is  a  metal, 

Every  metal  is  an  element, 
Therefore  Iron  is  an  element. — 


to  THE   THREE  PARTS  OF  [LESS 

<re  see  that  it  is  made  up  of  three  statements  or  asscr 
tions,  and  that  each  of  these  contains,  besides  minoi 
words,  two  nouns  substantive  or  names  of  things,  and  thf 
/erb  "is."  In  short,  two  names,  or  tenna,  when  connected 
^y  a  verb,  make  up  an  assertion  or  proposition ;  and 
Jiree  such  propositions  make  up  an  argument,  called  in 
this  case  a  iylloglnn.  Hence  it  is  natural  and  conve- 
nient first  to  describe  terms,  as  the  simplest  parts ;  next 
to  proceed  to  the  nature  and  varieties  of  propositions 
constructed  out  of  them,  and  then  we  shall  be  in  a  posi- 
tion to  treat  of  the  syllogism  as  a  whole.  Such  accord- 
ingly are  the  three  parts  of  logical  doctrine. 

But  though  we  may  say  that  the  three  parts  of  logic 
are  concerned  with  terms,  propositions,  and  syllogisms, 
it  may  be  said  with  equal  or  greater  truth  that  the  acts  of 
mind  indicated  by  those  forms  of  language  are  the  real 
subject  of  our  consideration.  The  opinions,  or  rather 
perhaps  the  expressions,  of  logicians  have  varied  on  this 
point  Archbishop  Whately  says  distinctly  that  logic  ii 
entirely  conversant  about  language;  Sir  W.  Hamilton,  Mr 
Mansel,  and  most  other  logicians  treat  it  as  concerned 
irith  the  acts  or  states  of  mind  indicated  by  the  words ; 
while  Mr  J.  S.  Mill  goes  back  to  the  things  themselves 
concerning  which  we  argue.  Is  the  subject  of  logic,  then, 
language,  thought,  or  ot>J«cts?  The  simplest  and  truest 
answer  is  to  say  that  it  treats  in  a  certain  sense  of  all 
three.  Inasmuch  as  no  reasoning  process  can  be  ex- 
plained or  communicated  to  another  person  without 
words,  we  are  practically  limited  to  such  reasoning  as  is 
reduced  to  the  form  of  language.  Hence  we  shall  always 
be  concerned  with  words,  but  only  so  far  as  they  are  the 
instruments  for  recording  and  referring  to  our  thoughts. 
The  grammarian  also  treats  of  language,  but  he  treats  it 
as  language  merely,  and  his  science  terminates  with  the 
description  and  explanation  of  the  forms,  varieties,  and 


ILl  LOGICAL  DOCTRINE.  t> 

relations  of  words.  Logic  also  treats  of  language,  but 
only  as  the  necessary  index  to  the  action  of  mind. 

Again,  so  long  as  we  think  correctly  we  must  think  ol 
things  as  they  are;  the  state  of  mind  within  us  must 
correspond  with  the  state  of  things  without  us  whenevet 
in  opportunity  arises  for  comparing  them.  It  is  im 
possible  and  inconceivable  that  iron  should  prove  not  to 
be  an  elementary  substance,  if  it  be  a  metal,  and  every 
metal  be  an  element.  We  cannot  suppose,  and  there  is 
no  reason  to  suppose,  that  by  the  constitution  of  the 
mind  we  are  obliged  to  think  of  things  differently  from 
the  manner  in  which  they  are.  If  then  we  may  assume 
that  things  really  agree  or  differ  according  as  by  correct 
logical  thought  we  are  induced  to  believe  they  will,  it 
does  not  seem  that  the  views  of  the  logicians  named  are 
irreconcileable.  We  treat  of  things  so  far  as  they  are  the 
objects  of  thought,  and  we  treat  of  language  so  far  as  it  is 
the  embodiment  of  thought.  If  the  reader  will  bear  this 
explanation  in  mind,  he  will  be  saved  from  some  per- 
plexity  when  he  proceeds  to  read  different  works  on  logic, 
and  finds  them  to  vary  exceedingly  in  the  mode  of  treat- 
ment, or  at  least  of  expression. 

If,  when  reduced  to  language,  there  be  three  parts  of 
logic,  terms,  propositions,  and  syllogisms,  there  must  be 
as  many  different  kinds  of  thought  or  operations  of  mind 
These  are  usually  called — 

1.  Simple  apprehension, 

2.  Judgment 

3.  Reasoning  or  discourse. 

The  first  of  these,  Simple  Apprehension,  is  the  act  ol 
Blind  by  which  we  merely  become  aware  of  something, 
or  have  a  notion,  idea,  or  impression  of  it  brought  into 
the  mind.  The  adjective  simple  means  apart  from  othei 
things,  and  apprehension  the  taking  hold  by  the  mind. 
Thus  the  name  or  term  Iron  instantaneously  makes  tbf 


I*  THE  THREE  PARTS  OF  [LESI 

mind  think  of  a  strong  and  very  useful  metal,  but  doe* 
not  tell  us  anything  about  it,  or  compare  it  with  any  thing 
zlse.  The  words  sun,  Jupiter,  Sirius,  St  PauPs  Cathe- 
dral, are  also  terms  which  call  up  into  the  mind  certain 
veil-known  objects,  which  dwell  in  our  recollection  even 
when  they  are  not  present  to  our  senses.  In  fact,  the  use 
of  a  term,  such  as  those  given  as  examples,  is  merely  as  a 
substitute  for  the  exhibition  of  the  actual  things  named. 

Judgment  is  a  different  action  of  mind,  and  consists  in 
comparing  together  two  notions  or  ideas  of  objects  de- 
rived from  simple  apprehension,  so  as  to  ascertain  whe- 
ther they  agree  or  differ.  It  is  evident,  therefore,  that  we 
cannot  judge  or  compare  unless  we  are  conscious  of  two 
things  or  have  the  notions  of  two  things  in  the  mind  at 
the  same  time.  Thus  if  I  compare  Jupiter  and  Sirius  I 
first  simply  apprehend  each  of  them ;  but  bringing  them 
into  comparison  I  observe  that  they  agree  in  being  small, 
bright,  shining  bodies,  which  rise  and  set  and  move 
round  the  heavens  with  apparently  equal  speed.  By 
minute  examination,  however,  I  notice  that  Sirius  gives 
a  twinkling  or  intermittent  light,  whereas  Jupiter  shines 
steadily.  More  prolonged  observation  shews  that  Ju- 
piter and  Sirius  do  not  really  move  with  equal  and 
regular  speed,  but  that  the  former  changes  its  position 
upon  the  heavens  from  night  to' night  in  no  very  simple 
manner.  If  the  comparison  be  extended  to  others  of  the 
heavenly  bodies  which  are  apprehended  or  seen  at  the 
same  time,  I  shall  find  that  there  are  a  multitude  of  stars 
which  agree  with  Sirius  in  giving  a  twinkling  light  and 
in  remaining  perfectly  fixed  hi  relative  position  to  each 
other,  whereas  two  or  three  other  bodies  may  be  seen 
which  resemble  Jupiter  in  giving  a  steady  light,  and  aljq 
in  changing  then-  place  from  night  to  night  among  the 
fixed  stars.  I  have  now  by  the  action  of  judgment 
formed  in  my  mind  the  general  notion  of  faced  start,  by 


a]  LOGICAL  DOCTRINE.  13 

bringing  together  mentally  a  number  of  objects  which 
'  agree  ;  while  from  several  other  objects  I  have  formed  the 
general  notion  ot  planets.  Comparing  the  two  genera] 
notions  together,  I  find  that  they  do  not  possess  the  same 
qualities  or  appearances,  which  I  state  in  the  proposition, 
!*  Planets  are  not  fixed  stars." 

I  have  introduced  the  expression  "General  Notion"  as 
if  the  reader  were  fully  acquainted  with  it.  But  though 
pnilosophers  have  for  more  than  two  thousand  years  con- 
stantly used  the  expressions,  general  notion,  idea,  con- 
ception, concept,  &c.,  they  have  never  succeeded  in 
agreeing  exactly  as  to  the  meaning  of  the  terms.  One 
class  of  philosophers  called  Nominalists  say  that  it  is  all  a 
matter  of  names,  and  that  when  we  join  together  Jupiter, 
Mars,  Saturn,  Venus,  &c.,  and  call  them  planets,  the 
common  name  is  the  bond  between  them  in  our  minds. 
Others,  called  Realists,  have  asserted  that  besides  these 
particular  planets  there  really  is  something  which  com- 
bines the  properties  common  to  them  all  without  any  of 
the  differences  of  size,  colour,  or  motion  which  distin- 
guish them.  Every  one  allows  in  the  present  day  how- 
ever that  nothing  can  physically  exist  corresponding  to  a 
general  notion,  because  it  must  exist  here  or  there,  of  this 
size  or  of  that  size,  and  therefore  it  would  be  one  particu- 
lar planet,  and  not  any  planet  whatever.  The  Nominal- 
ists, too,  seem  equally  wrong,  because  language,  to  be  of 
any  use,  must  denote  something,  and  must  correspond,  as 
we  have  seen,  to  acts  of  mind.  If  then  proper  names 
raise  up  in  our  minds  the  images  of  particular  things,  like 
the  sun,  Jupiter,  &c.,  general  names  should  raise  up 
general  notions. 

The  true  opinion  seems  to  be  that  of  the  philoso- 
phers called  Conceptualists,  who  say  that  the  general  no« 
don  is  the  knowledge  in  the  mind  of  the  common  pro- 
perties or  resemblances  of  the  things  embraced  undet 


14  THE  THREE  PARTS  OF  [l 

the  notion.  Thus  the  notion  planet  really  means  the 
consciousness  in  anybody's  mind  that  there  are  certain 
heavenly  bodies  which  agree  in  giving  a  steady  light 
and  in  moving  about  the  heavens  differently  from  thi 
axed  stars.  It  should  be  added,  however,  that  there  art 
many,  including  Sir  W.  Hamilton,  who  would  be  counted 
as  Nominalists  and  who  yet  hold  that  with  the  general 
name  is  associated  a  consciousness  of  the  resemblance 
existing  between  the  things  denoted  by  it.  Between  this 
form  of  the  doctrine  and  conceptualism  it  is  not  easy  to 
draw  a  precise  distinction,  and  the  subject  is  of  too  de- 
batable a  character  to  be  pursued  in  this  work. 

It  will  appear  in  the  course  of  these  lessons  that  the 
whole  of  logic  and  the  whole  of  any  science  consists  in  so 
arranging  the  individual  things  we  meet  in  general  no- 
tions or  classes,  and  in  giving  them  appropriate  general 
names  or  terms,  that  our  knowledge  of  them  may  be 
made  as  simple  and  general  as  possible.  Every  general 
notion  that  is  properly  formed  admits  of  the  statement  of 
general  laws  or  truths ;  thus  of  the  planets  we  may  affirm 
that  they  move  in  elliptic  orbits  round  the  sun  from  west 
to  east ;  that  they  shine  with  the  reflected  light  of  the 
sun ;  and  so  on.  Of  the  fixed  stars  we  may  affirm  that 
they  shine  with  their  own  proper  light;  that  they  are 
incomparably  more  distant  than  the  planets ;  and  so  on 
The  whole  of  reasoning  will  be  found  to  arise  from  this 
faculty  of  judgment,  which  enables  us  to  discover  and 
affirm  that  a  large  number  of  objects  have  similar  pro 
pertief,  so  that  whatever  is  known  of  some  may  be  in 
lerred  and  asserted  of  others. 

It  is  in  the  application  of  such  knowledge  that  w< 
onploy  the  third  act  of  mind  called  discourse  or  reason 
dig,  by  which  from  certain  judgments  we  are  enabled, 
without  any  new  reference  to  the  real  objects,  to  form  * 
new  judgment  If  we  know  that  iron  comes  under  th« 


n.J  LOGICAL  DOCTRINE.  1} 

general  notion  of  metal,  and  that  this  notion  comes  under 
the  still  wider  notion  of  element,  then  without  furthei 
examination  of  iron  we  know  that  it  is  a  simple  unde 
composable  substance  called  by  chemists  an  element.  Oi 
if  from  one  source  of  information  we  learn  that  Neptun* 
is  a  planet,  and  from  another  that  planets  move  in  ellip 
tic  orbits,  we  can  join  these  two  portions  of  knowledge 
together  in  the  mind,  so  as  to  elicit  the  truth  that  Nep- 
tune moves  in  an  elliptic  orbit. 

Reasoning  or  Discourse,  then,  may  be  defined  as  .he 
progress  of  the  mind  from  one  or  more  given  propositions 
to  a  proposition  different  from  those  given.  Those  pro- 
positions from  which  we  argue  are  called  Premises,  and 
that  which  is  drawn  from  them  is  called  the  Conclusion, 
The  latter  is  said  to  follow,  to  be  concluded,  inferred  or  col- 
lected from  them ;  and  the  premises  are  so  called  because 
they  are  put  forward  or  at  the  beginning  (Latin  pra,  be- 
fore, and  mitto,  I  send  or  put).  The  essence  of  the  pro- 
cess consists  in  gathering  the  truth  that  is  contained  in 
the  premises  when  joined  together,  and  carrying  it  with 
us  into  the  conclusion,  where  it  is  embodied  in  a  new 
proposition  or  assertion.  We  extract  out  of  the  pre- 
mises all  the  information  which  is  useful  for  the  purpose 
in  view — and  this  is  the  whole  which  reasoning  accom- 
plishes. 

I  have  now  pointed  out  the  three  parts  of  logical  doc- 
trine, Terms,  Propositions,  and  Reasoning  or  Syllogism, 
into  which  the  subject  is  conveniently  divided.  To  the 
consideration  of  these  parts  we  shall  proceed  But  it 
may  be  mentioned  that  a  fourth  part  has  often  been 
added  called  Method,  which  is  concerned  with  the  ar- 
rangement of  the  parts  of  any  composition. 

It  is  sometimes  said  that  what  proposition  is  to  term, 
and  what  syllogism  is  to  proposition,  such  is  method  to 
syllogism,  and  that  a  fourth  division  is  necessary  to  com* 


16  TERMS,  AND   THEIR  [l 

plcte  the  doctrine  of  Logic.  It  is  at  any  rate  ccrtaii 
however  that  this  fourth  part  is  much  inferior  in  import- 
ance and  distinctness  to  the  preceding  three ;  and  all  thai 
will  be  s&id  of  it  is  to  be  found  in  Lesson  xxrv, 


LESSON  IIL 
TERMS,  AND  THEIR  VARIOUS   KINDS. 

IT  has  been  explained  in  the  preceding  lesson  that  ever) 
assertion  or  statement  expresses  the  agreement  or  dif- 
ference of  two  things,  or  of  two  general  notions.  In 
putting  the  assertion  or  statement  into  words,  we  must 
accordingly  have  words  suitable  for  drawing  the  attention 
of  the  mind  to  the  things  which  are  compared,  as  well  as 
words  indicating  the  result  of  the  comparison,  that  is  to 
say,  the  fact  whether  they  agree  or  differ.  The  words  by 
which  we  point  out  the  things  or  classes  of  things  in 
question  are  called  Terms,  and  the  words  denoting  the 
comparison  are  said  to  form  the  Copula.  Hence  a  com- 
plete assertion  or  statement  consists  of  two  terms  and  a 
copula,  and  when  thus  expressed  it  forms  a  Proposition. 
Thus  in  the  proposition  "  Dictionaries  are  useful  books," 
the  two  terms  are  dictionaries  and  useful  books;  the  co- 
pula is  the  verb  are,  and  expresses  a  certain  agreement  ol 
the  class  dictionaries  with  the  class  of  useful  books  con- 
sisting in  the  fact  that  the  class  of  dictionaries  forms  part 
of  the  class  of  useful  books.  In  this  case  each  term  con- 
sists of  only  one  or  two  words,  but  any  number  of  words 
nay  be  required  to  describe  the  notions  or  classes  com- 


III.]  VARIOUS  KINDS.  17 

pared  together.  In  the  proposition  "the  angles  at  the 
base  of  an  isosceles  triangle  are  equal  to  each  other,7*  the 
first  term  requires  nine  words  for  its  expression,  and  the 
second  term,  four  words  (equal  to  each  other);  and  tLere 
is  no  limit  to  the  number  of  words  which  may  be  em- 
ployed in  the  formation  of  a  term. 

A  term  is  so  called  because  it  forms  one  end  (Latin, 
tt*-minus)  of  a  proposition,  and  strictly  speaking  it  is  a 
term  only  so  long  as  it  stands  in  the  proposition.  But 
we  commonly  speak  of  a  term  or  a  name  meaning  any 
noun,  substantive  or  adjective,  or  any  combination  of 
words  denoting  an  object  of  thought,  whether  that  be,  as 
we  shall  shortly  see,  an  individual  thing,  a  group  of  things, 
a  quality  of  things,  or  a  group  of  qualities.  It  would  be 
impossible  to  define  a  name  or  term  better  than  has  been 
done  by  Hobbes :  "A  name  is  a  word  taken  at  pleasure 
to  serve  for  a  mark,  which  may  raise  in  our  mind  a 
thought  like  to  some  thought  which  we  had  before,  and 
which,  being  pronounced  to  others,  may  be  to  them  a 
sign  of  what  thought  the  speaker  had  before  in  his  mind." 

Though  every  term  or  name  consists  of  words  it  is 
not  every  word  which  can  form  a  name  by  itself.  We 
cannot  properly  say  "  Not  is  agreeable"  or  "  Probably  is 
not  true  f  nothing  can  be  asserted  of  a  preposition,  an 
adverb,  and  certain  other  parts  of  speech,  except  indeed 
that  they  are  prepositions,  adverbs,  &c.  No  part  of 
speech  except  a  noun  substantive,  or  a  group  of  words 
used  as  a  noun  substantive,  can  form  the  subject  or  first 
term  of  a  proposition,  and  nothing  but  a  noun  substan- 
tive, an  adjective,  the  equivalent  of  an  adjective,  or  a 
yerb,  can  form  the  second  term  or  predicate  of  a  propo- 
sition It  may  indeed  be  questioned  whether  an  adjec 
live  can  ever  form  a  term  alone ;  thus  in  "  Dictionaries 
are  useful,"  it  may  be  said  that  the  substantive  things  of 
books  is  understood  in  the  predicate,  the  complete  sen* 

9 


it  TERMS,  AND   THEIR  [LESS 

fence  being  "  Dictionaries  are  useful  books f  but  as  this 
is  a  disputed  point  we  will  assume  that  words  are  divided 
into  two  kinds  in  the  following  manner : — 

Words  which  stand,  or  appear  to  stand  alone  as  com- 
plete terms,  namely  the  substantive  and  adjective,  and 
certain  parts  of  a  verb,  are  called  categorematlc  words 
from  the  Greek  word  rar^yopcw,  to  assert  or  predicate. 

Those  parts  of  speech,  on  the  other  hand,  such  a* 
prepositions,  adverbs,  conjunctions,  &c,  which  can  only 
form  parts  of  names  or  terms  are  called  syncategorematio 
words,  because  they  must  be  used  with  other  words  in 
order  to  compose  terms  (Greek  <n5»»,  with,  and  Karrjyopc*). 
Of  syncategorematic  words  we  need  not  take  further 
notice  except  so  far  as  they  form  part  of  categorematic 
terms. 

We  have  now  to  consider  the  various  kinds  and  pecu- 
liarities of  terms,  so  as  to  gain  a  clear  idea  of  what  they 
mean.  Terms  are  first  of  all  distinguished  into  singular 
or  individual,  and  general  or  common  terms,  this  being  a 
very  obvious  division,  but  one  of  much  importance.  A 
Singular  term  is  one  which  can  denote  only  a  single  ob- 
ject, so  long  at  least  as  it  is  used  in  exactly  the  same 
meaning ;  thus  the  Emperor  of  the  French,  the  Atlantic 
Ocean,  St  Paul's,  William  Shakspeare,  the  most  pre- 
cious of  the  metals,  are  singular  terms.  All  proper  names 
belong  to  this  class;  for  though  John  Jones  is  the  name 
of  many  men,  yet  it  is  used  not  as  meaning  any  of  these 
men,  but  some  single  man— it  has,  in  short,  a  differem 
meaning  in  each  case,  just  as  London,  the  name  of  oui 
capital,  has  no  connexion  in  meaning  with  London  io 
Canada. 

Ctoneral  term*,  on  the  contrary,  are  applicable  in  the 
tame  sense  equally  to  any  one  of  an  indefinite  number  of 
•bjects  which  resemble  each  other  in  certain  qualities. 
Thus  maml  is  a  general  name  because  it  may  be  applied 


ill.]  VARIOUS  KINDS.  19 

indifferently  to  gold,  silver,  copper,  tin,  aluminium,  or  any 
of  about  fifty  known  substances.  It  is  not  the  name  of 
any  one  of  these  more  than  any  other,  and  it  is  in  fac 
applied  to  any  substance  which  possesses  metallic  lustre 
which  cannot  be  decomposed,  and  which  has  certain 
other  qualities  easily  recognised  by  chemists.  Nor  is  the 
number  of  substances  in  the  class  restricted;  for  as  new 
kinds  of  metal  are  from  time  to  time  discovered  they  are 
added  to  the  class.  Again,  while  Mars,  Jupiter,  Saturn, 
&c.,  are  singular  terms,  since  each  can  denote  only  a 
single  planet,  the  term  planet  is  a  general  one,  being 
applicable  to  as  many  bodies  as  may  be  discovered  to 
revolve  round  the  sun  as  the  earth  does. 

We  must  carefully  avoid  any  confusion  between  ge- 
neral and  collective  terms.  By  a  collective  term  we 
mean  the  name  of  a  number  of  things  when  all  joined 
together  as  one  whole  ;  like  the  soldiers  of  a  regiment, 
the  men  of  a  jury,  the  crew  of  a  vessel :  thus  a  collective 
term  is  the  name  of  all,  but  not  of  each.  A  general  term, 
on  the  other  hand,  is  the  name  of  a  number  of  things, 
but  of  each  of  them  separately,  or,  to  use  the  technical 
expression,  distributively.  Soldier,  juryman,  sailor,  are 
the  general  names  which  may  belong  to  John  Jones. 
Thomas  Brown,  &c.,  but  we  cannot  say  that  John  Jonei 
is  a  regiment,  Thomas  Brown  a  jury,  and  so  on.  The 
distinction  is  exceedingly  obvious  when  thus  pointed  out, 
but  it  may  present  itself  in  more  obscure  forms,  and  is 
then  likely  to  produce  erroneous  reasoning,  as  will  'oe 
pointed  out  in  Lesson  xx.  It  is  easy  to  see  that  we  must 
not  divide  terms  into  those  which  are  general  and  those 
which  are  collective,  because  it  will  often  happen  that 
the  same  term  is  both  general  and  collective,  according 
as  it  is  regarded.  Thus,  library  is  collective  as  regards 
the  books  in  it,  but  is  general  as  regards  the  great  num 
ter  of  different  libraries,  private  or  public,  which  exist 


*.  TERMS.  AND    THEIR 

Regiment  is  a  collective  term  as  regards  the  soldicn 
which  compose  it,  but  general  as  regards  the  hundred 
different  regiments,  the  Coldstream  Guards,  the  High 
land  regiment,  the  Welsh  Fusiliers,  and  the  rest,  which 
compose  the  British  standing  army.  Army,  again,  is  a 
collective  whole,  as  being  composed  of  a  number  of  regi- 
ments organized  together.  Year  is  collective  as  regards 
the  months,  weeks,  or  days  of  which  it  consists,  but  is 
general  as  being  the  name  either  of  1869  or  1870,  or  any 
period  marked  by  a  revolution  of  the  earth  round  the  sun. 

We  have  not  always  in  the  English  language  suffi- 
cient means  of  distinguishing  conveniently  between  the 
general  and  collective  use  of  terms.  In  Latin  this  dis- 
tinctive use  was  exactly  expressed  by  omnes,  meaning  all 
distributively,  and  cuncti  meaning  all  taken  together,  a 
contracted  form  of  conjuncti  (joined  together).  In  English 
all  nun  may  mean  any  man  or  all  men  together.  Even 
the  more  exact  word  every  is  sometimes  misused,  as  in 
the  old  proverb,  '  Every  little  makes  a  mickle,'  where  it  is 
obvious  that  every  little  portion  cannot  by  itself  make 
much,  but  only  when  joined  to  other  little  portions. 

A  second  important  distinction  between  terms  is  that 
of  concrete  terms  and  abstract  terms ;  and  it  cannot  be 
better  described  than  in  the  words  of  Mr  Mill,  by  saying 
that  a  concrete  name  is  the  name  of  a  thing,  the  abstract 
name  is  the  name  of  a  quality,  attribute,  or  circumstance 
of  a  thing.  Thus  red  house  is  the  name  of  a  physically- 
existing  thing,  and  is  concrete;  redness  is  the  name  of 
one  quality  of  the  house,  and  is  abstract.  The  word 
abstract  means  drawn  from  (Latin,  abstractus,  from  abs- 
inhere,  to  draw  away  from),  and  indicates  that  the  quality 
redness  is  thought  of  in  the  mind  apart  from  all  the  other 
fualities  which  belong  to  the  red  house,  or  other  red 
abject  But  though  we  can  think  of  a  quality  by  itself 
ft*  cannot  suppose  that  the  quality  can  exist  physically 


riL]  VARIOUS   KINDS  11 

apart  from  the  matter  in  which  it  is  manifest  to  us.  Red- 
ness  means  either  a  notion  in  the  mind,  or  it  means  that 
in  red  objects  which  excites  the  notion. 

The  reader  should  carefully  observe  that  adjective* 
are  concrete,  not  abstract.  If  we  say  that  a  book  is  use- 
ful, it  is  to  the  book  we  apply  the  adjective  useful,  and 
usefulness  is  the  abstract  noun  which  denotes  the  quality ; 
similarly,  the  adjectives  equal,  grateful,  reverent,  ratio- 
nal, are  the  names  of  things,  and  the  corresponding  abs- 
tract nouns  are  equality,  gratitude,  reverence,  rationality. 
This  distinction  will  become  more  apparent  in  reading 
Lesson  v. 

It  is  a  good  exercise  to  try  and  discover  pairs  of  cor- 
responding concrete  and  abstract  names  ;  thus  animal 
has  animality ;  miser,  miserliness  ;  old,  agedness,  or  old 
age  ;  substance,  substantiality ;  soap,  soapiness ;  shrub, 
shrubbiness  ;  and  so  on.  But  it  by  no  means  follows  that 
an  abstract  word  exists  for  each  concrete ;  table  hardly  has 
an  abstract  tabularity ;  and  though  ink  has  inkiness,  we 
should  not  find  the  abstract  of  pen.  It  is  by  the  accidents 
of  the  history  of  language  that  we  do  or  do  not  possess 
abstract  names ;  and  there  is  a  constant  tendency  to  in- 
vent new  abstract  words  in  the  progress  of  time  and 
science. 

Unfortunately  concrete  and  abstract  names  are  fre- 
quently confused,  and  it  is  by  no  means  always  easy  to 
distinguish  the  meanings.  Thus  relation  properly  is  the 
abstract  name  for  the  position  of  two  people  or  things  to 
each  other,  and  those  people  are  properly  called  relative! 
(Latin,  relativus,  one  who  is  related).  But  we  constantly 
speak  now  of  relations,  meaning  the  persons  themselves ; 
and  when  we  want  to  indicate  the  abstract  relation 
they  have  to  each  other  we  have  to  invent  a  new  abstract 
name  relationship.  Nation  has  long  been  a  concrete 
Verm,  though  from  its  form  it  was  probably  abstract  at 


ta  TERMS,  AND  THEIR  [LESS 

tirst ;  but  so  far  does  the  abuse  of  language  now  go, 
especially  in  newspaper  writing,  that  we  hear  of  a  nation- 
ality meaning  a  nation,  although  of  course  if  nation  is 
the  concrete,  nationality  ought  to  be  the  abstract,  mean 
ing  the  quality  of  being  a  nation.  Similarly,  action, 
intention,  extension,  conception,  and  a  multitude  of  other 
properly  abstract  names,  are  used  confusedly  for  the  corre- 
sponding concrete,  namely,  act,  intent,  extent,  concept,  &c. 
Production  is  properly  the  condition  or  state  of  a  person 
who  is  producing  or  drawing  something  forth  ;  but  it  has 
now  become  confused  with  that  which  is  produced,  so 
that  we  constantly  talk  of  the  production's  of  a  country, 
meaning  the  products.  The  logical  terms,  Proposition, 
Deduction,  Induction,  Syllogism,  are  all  properly  abstract 
words,  but  are  used  concretely  for  a  Proposition,  a  De- 
duction, an  Induction,  a  Syllogism ;  and  it  must  be  al- 
lowed that  logicians  are  nearly  as  bad  as  other  people  in 
confusing  abstract  and  concrete  terms.  Much  injury  is 
done  to  language  by  this  abuse. 

Another  very  obvious  division  of  terms  is  between 
those  which  are  positive,  and  those  which  are  negative. 
The  difference  is  usually  described  by  saying  that  posi- 
tive terms  signify  the  existence  or  possession  of  a  quality, 
as  in  grateful,  metallic,  organic,  etc.,  while  the  correspond- 
ing negatives  signify  the  absence  of  the  same  qualities 
as  in  ungrateful,  non-metallic,  inorganic.  The  negative 
terms  may  be  adjectives  as  above,  AT  substantives,  con- 
crete or  abstract  ;  thus  ingratitude,  inequality,  incon- 
venience are  abstract  negative  terms;  and  individuals, 
unequals,  &c.  are  concrete  negatives  We  usually  consider 
as  negative  terms  any  which  have  a  negative  prefix  such 
is  not,  non,  un,  in,  &c. ;  but  there  are  a  great  many  terms 
which  serve  as  negatives  without  possessing  any  mark  of 
their  negative  character.  Darkness  is  the  negative  (A 
light  or  lightness,  since  it  means  the  absence  of  light: 


in.]  VARIOUS  KINDS.  23 

compound  is  the  negative  of  element,  since  we  should 
give  the  name  of  compound  to  whatever  can  be  decom* 
posed,  and  element  is  what  cannot  be  decomposed  ;  theo- 
retically speaking  every  term  has  its  corresponding  nega- 
tive, but  it  by  no  means  follows  that  language  furnishes 
the  term  ready-made.  Thus  table  has  the  corresponding 
adjective  tabular,  but  there  is  no  similar  negative  untabu- 
lar ;  one  man  may  be  called  a  bookworm,  but  there  is  no 
negative  for  those  who  are  not  bookworms,  because  no 
need  of  the  expression  has  been  felt.  A  constant  process 
of  invention  of  new  negative  terms  goes  on  more  rapidly 
perhaps  than  is  desirable,  for  when  an  idea  is  not  often 
referred  to  it  is  better  to  express  it  by  a  phrase  than  add 
to  the  length  of  the  dictionary  by  a  new-created  word. 

It  would  seem  that  in  many  cases  a  negative  term 
implies  the  presence  of  some  distinct  quality  or  fact. 
Thus  inconvenience  doubtless  implies  the  absence  of 
convenience,  but  also  the  presence  of  positive  trouble  or 
pain  occasioned  thereby.  Unhappiness  is  a  negative 
term,  but  precisely  the  same  notion  is  expressed  by  the 
positive  term  misery.  The  negative  of  healthy  is  un- 
healthy, but  the  positive  term  sickly  serves  equally  well. 
It  thus  appears  to  be  more  a  matter  of  accident  than 
anything  else  whether  a  positive  or  negative  term  is  used 
to  express  any  particular  notion.  All  that  we  can  really 
say  is  that  every  positive  term  necessarily  implies  the 
existence  of  a  corresponding  negative  term,  which  may  be 
the  name  of  all  those  things  to  which  the  positive  name 
cannot  be  applied.  Whether  this  term  has  been  invented 
or  not  is  an  accident  of  language :  its  existence  may  be 
assumed  in  logic. 

The  reader  may  be  cautioned  against  supposing  that 
every  term  appearing  to  be  of  a  negative  character  on 
account  of  possessing  a  negative  prefix  is  really  so.  The 
participle  unloosed  certainly  appears  to  be  the  negative  of 


AND    THEIR  [LESS. 

loosed;  out  the  two  words  mean  exactly  the  same  thing, 
the  prefix  un  not  being  really  the  negative;  invaluable^ 
again,  means  not  what  is  devoid  of  value,  but  what  is  so 
valuable  that  the  value  cannot  be  measured;  and  a 
hameless  action  can  equally  be  called  by  the  positive 
term,  a  shameful  action.  Other  instances  might  no 
doubt  be  found. 

Great  care  should  be  taken  to  avoid  confusing  terms 
which  express  the  presence  or  absence  of  a  quality  with 
those  which  describe  its  degree.  Less  is  not  the  negative 
si  greater  because  there  is  a  third  alternative,  equal.  The 
true  negative  of  greater  is  not-greater,  and  this  is  equiva- 
lent to  either  equal  or  less.  So  it  may  be  said  that  dis- 
agreeable is  not  the  simple  negative  of  agreeable,  because 
there  may  be  things  which  are  neither  one  nor  the  other, 
but  are  indifferent  to  us.  It  would  not  be  easy  to  say 
offhand  whether  every  action  which  is  not  honest  is  dis- 
honest, or  whether  there  may  not  be  actions  of  an  inter- 
mediate character.  The  rule  is  that  wherever  the  question 
is  one  of  degree  or  quantity  a  medium  is  possible,  and 
the  subject  belongs  rather  to  the  science  of  quantity 
than  to  simple  logic ;  where  the  question  is  one  of  the 
presence  or  absence  of  a  quality,  there  cannot  be  more 
than  two  alternatives,  according  to  one  of  the  Primary 
Laws  of  Thought,  which  we  will  consider  in  Lesson  XIV. 
In  the  case  of  quantity  we  may  call  the  extreme  terms 
opposltes ;  thus  less  is  the  opposite  of  greater,  disagreeable 
of  agreeable ;  in  the  case  of  mere  negation  we  may  call 
the  terms  negatives  or  contradictories,  and  it  is  really 
indifferent  in  a  logical  point  of  view  which  of  a  pair  ol 
contradictory  terms  we  regard  as  the  positive  and  which 
is  the  negative.  Each  is  the  negative  of  the  other. 

Logicians  have  distinguished  from  simple  negative 
terms  a  class  of  terms  called  privative,  such  as  blind^ 
Such  terms  express  that  a  thing  has  beec 


HLJ  VARIOUS  KINDS.  25 

deprived  of  a  quality  which  it  before  possessed,  or  was 
capable  of  possessing,  or  usually  does  possess.  A  man 
may  be  born  blind,  so  that  he  never  did  see,  but  he  pos- 
sesses the  organs  which  would  have  enabled  him  to  se€ 
except  for  some  accident.  A  stone  or  a  tree  could  not 
have  had  the  faculty  of  seeing  under  any  circumstances. 
No  mineral  substance  can  properly  be  said  to  die  or  tc 
be  dead,  because  it  was  incapable  of  life ;  but  it  may  be 
called  uncrystallized  because  it  might  hare  been  in  the 
form  of  a  crystal  Hence  we  apply  a  privative  term  to 
anything  which  has  not  a  quality  which  it  was  capable  of 
having ;  we  apply  a  negative  term  to  anything  which  has 
not  and  could  not  have  the  quality.  It  is  doubtful  however 
whether  this  distinction  can  be  properly  carried  out,  and 
it  is  not  of  very  much  importance. 

It  is  further  usual  to  divide  terms  according  as  they 
are  relative  or  absolute,  that  is,  non-relative.  The  adjective 
absolute  means  whatever  is  "loosed  from  connection 
with  anything  else"  (Latin  ab,  from,  and  sotufus,  loosed); 
whereas  relative  means  that  which  is  carried  in  thought, 
at  least,  into  connection  with  something  else.  Hence  a 
relative  term  denotes  an  object  which  cannot  be  thought 
of  without  reference  to  some  other  object,  or  as  part  of  a 
larger  whole.  A  father  cannot  be  thought  of  but  in  rela- 
tion to  a  child,  a  monarch  in  relation  to  a  subject,  a  shep- 
herd in  relation  to  a  flock;  thus  father,  monarch,  and 
shepherd  are  relative  terms,  while  child,  subject,  and 
flock  are  the  correlatives  (Latin  con,  with,  and  relativus), 
or  those  objects  which  are  necessarily  joined  in  thought 
with  the  original  objects.  The  very  meaning,  in  fact,  of 
father  is  that  he  has  a  child,  of  monarch  that  he  has 
subjects,  and  of  shepherd  that  he  has  a  flock.  As  ex- 
amples of  terms  which  have  no  apparent  relation  to  any- 
thing else,  I  may  mention  water,  gas,  tree.  There  doei 
not  seem  to  me  to  be  anything  so  habitually  associated 


26  TERMS,  AND   THEIR  [LESS. 

with  water  that  we  must  think  of  it  as  part  of  the  same 
idea,  and  gas,  tree,  and  a  multitude  of  other  terms,  also 
denote  objects  which  have  no  remarkable  or  permanent 
relations  such  as  would  entitle  the  terms  to  be  called  rela- 
tives. They  may  therefore  be  considered  absolute  or 
non-relative  terms. 

The  fact,  however,  is  that  everything  must  really  have 
relations  to  something  else,  the  water  to  the  elements  of 
which  it  is  composed,  the  gas  to  the  coal  from  which  it  is 
manufactured,  the  tree  to  the  soil  in  which  it  is  rooted. 
By  the  very  laws  of  thought,  again,  no  thing  or  class  of 
things  can  be  thought  of  but  by  separating  them  from 
other  existing  things  from  which  they  differ.  I  cannot  use 
the  term  mortal  without  at  once  separating  all  existing 
or  conceivable  things  into  the  two  groups  mortal  and 
immortal]  metal,  element,  organic  substance,  and  every 
other  term  that  could  be  mentioned,  would  necessarily 
imply  the  existence  of  a  correlative  negative  term,  non- 
metallic,  compound,  inorganic  substance,  and  in  this 
respect  therefore  every  term  is  undoubtedly  relative. 
Logicians,  however,  have  been  content  to  consider  as 
relative  terms  those  only  which  imply  some  peculiar  and 
striking  kind  of  relation  arising  from  position  in  time  or 
space,  from  connexion  of  cause  and  effect,  &c. ;  and  it 
is  in  this  special  sense  therefore  the  student  must  use  the 
distinction. 

The  most  important  varieties  of  terms  having  been 
explained,  it  is  desirable  that  the  reader  should  acquire  a 
complete  familiarity  with  them  by  employing  the  exercises 
at  the  end  of  the  book.  The  reader  is  to  determine  con- 
cerning each  of  the  terms  there  given  :  — 

1.  Whether  it  is  a  categorematic  or  syncategore 

matic  term. 

2.  Whether  it  is  a  general  or  a  singular  term. 

3.  Whether  it  is  collective  or  distributive. 


OL]  VARIOUS  KINDS.  z> 

4.  Whether  it  is  concrete  or  abstract 

5.  Whether  it  is  positive,  or  negative,  or  privative. 

6.  Whether  it  is  relative  or  absolute. 

It  will  be  fully  pointed  out  in  the  next  lesson  *K«* 
most  terms  have  more  than  one  meaning;  and  as  the  one 
meaning  may  be  general  and  the  other  singular,  the  one 
concrete  and  the  other  abstract,  and  so  on,  it  is  absolute- 
ly necessary  that  the  reader  should  first  of  all  choos* 
one  precise  meaning  of  the  term  which  he  is  examining. 
And  in  answering  the  questions  proposed  it  is  desirable 
he  should  specify  the  way  in  which  he  regards  it  Taking 
the  word  sovereign,  we  may  first  select  the  meaning  in 
which  it  is  equivalent  to  monarch ;  this  is  a  general  term 
in  so  far  as  it  is  the  name  of  any  one  of  many  monarch) 
living  or  dead,  but  it  is  singular  as  regards  the  inhabit- 
ants of  any  one  country.  It  is  clearly  categorematic, 
concrete,  and  positive,  and  obviously  relative  to  the  sub- 
jects of  the  monarch. 

Read  Mr  Mill's  chapter  on  Namts,  System  of  Logic 
Book  I.  chap.  2. 


LESSON  IV. 

OF  THE  AMBIGUITY  OF  TERMS. 


'HERE  is  no  part  of  Logic  which  is  more  really  useful 
than  that  which  treats  of  the  ambiguity  of  terms,  that  is 
of  the  uncertainty  and  variety  of  meanings  belonging  to 
irords.  Nothing  indeed  can  be  of  more  importance  to 
the  attainment  of  correct  habits  of  thinking  and  reason- 
ing than  a  thorough  acquaintance  with  the  great  imper- 
fections of  language.  Comparatively  few  terms  have  one 


98  OF  THE  AMBIGUITY  [LESS 

single  clear  meaning  and  one  meaning  only,  and  when 
ever  two  or  more  meanings  are  unconsciously  confuseo 
together,  we  inevitably  commit  a  logical  fallacy.  If,  foi 
instance,  a  person  should  argue  that  "  punishment  is  ar 
evil,"  and  according  to  the  principles  of  morality  "nc 
evil  is  to  be  allowed  even  with  the  purpose  of  doing 
good,"  we  might  not  at  the  first  moment  see  how  to  avoid 
the  conclusion  that  "  no  punishments  should  be  allowed/ 
because  they  cause  evil.  A  little  reflection  will  show  that 
the  word  evil  is  here  used  in  two  totally  different  senses 
in  the  first  case  it  means  physical  evil  or  pain ;  in  the 
second  moral  evil,  and  because  moral  evil  is  never  to  be 
committed,  it  does  not  follow  that  physical  evils  are  never 
to  be  inflicted,  for  they  are  often  the  very  means  of  pre- 
venting moral  evil./ 

Another  very  plausible  fallacy  which  has  often  been 
put  forth  in  various  forms  is  as  follows :  "  A  thoroughly 
benevolent  man  cannot  possibly  refuse  to  relieve  the  poo*", 
and  since  a  person  who  cannot  possibly  act  otherwise 
than  he  does  can  claim  no  merit  for  his  actions,  it  follows 
that  a  thoroughly  benevolent  man  can  claim  no  merit  for 
his  actions."  According  to  this  kind  of  argument  a  man 
would  have  less  merit  in  proportion  as  he  was  more 
virtuous,  so  as  to  feel  greater  and  greater  difficulty  in 
acting  wrongly.  That  the  conclusion  is  fallacious  every 
one  must  feel  certain,  but  the  cause  of  the  fallacy  can 
only  be  detected  by  observing  that  the  words  cannot 
possibly  have  a  double  meaning,  in  the  first  case  referring 
to  the  influence  of  moral  motives  or  good  character,  and 
ra  the  second  to  circumstances  entirely  beyond  a  person's 
control ;  as,  for  instance,  the  compulsion  of  the  laws,  the 
want  of  money,  the  absence  of  personal  liberty.  The 
more  a  person  studies  the  subtle  variations  in  the  mean- 
ing of  common  words,  the  more  he  will  be  convinced  oi 
the  dangerous  natuie  of  the  tools  he  has  to  use  in  alJ 


«V.j  OF  TERMS.  * 

communications   and  arguments.      Hence   I   must  ash 
much  attention  to  the  contents  of  this  Lesson. 

Terms  are  said  to  be  tmlvocal  when  they  can  suggesi 
to  the  mind  no  more  than  one  single  definite  meaning 
They  are  called  equivocal  or  ambiguous  when  they  \\.\\ 
two  or  more  different  meanings.  It  will  be  observe, 
however,  that  a  term  is  not  equivocal  because  it  can  !•< 
applied  to  many  objects  when  it  is  applied  in  the  same 
sense  or  meaning  to  those  different  objects.  Thus  cathe- 
dral is  the  name  of  St  Paul's,  the  York  Minster,  and  the 
principal  churches  of  Salisbury,  Wells,  Lincoln  and  a 
number  of  other  cities,  but  it  is  not  ambiguous,  because 
all  these  are  only  various  instances  of  the  same  meaning  ; 
they  are  all  objects  of  the  same  description  or  kind. 
The  word  cathedral  is  probably  univocal  or  of  one  logical 
meaning  only.  The  word  church,  on  the  other  hand,  is 
equivocal,  because  it  sometimes  means  the  building  in 
which  religious  worship  is  performed,  sometimes  the  body 
of  persons  who  belong  to  one  sect  or  persuasion,  and 
assemble  in  churches.  Sometimes  also  the  church 
means  the  body  of  the  clergy  as  distinguished  from  the 
laity;  hence  there  is  a  clear  difference  in  the  sense  or 
meaning  with  which  the  word  is  used  at  different  times. 

Instances  of  univocal  terms  are  to  be  found  chiefly  ID 
technical  and  scientific  language.  Steam-engine,  gas- 
ometer, railway  train,  permanent  way,  and  multitudes  of 
such  technical  names  denoting  distinct  common  objects, 
are  sufficiently  univocal.  In  common  life  the  names 
penny,  mantelpiece,  teacup,  bread  and  butter,  have  a  suf- 
ficiently definite  and  single  meaning.  So  also  in  chemistry, 
oxygen,  hydrogen,  sulphate  of  copper,  alumina,  lithia, 
ind  thousands  of  other  terms,  are  very  precise,  the  words 
themselves  having  often  been  invented  in  very  recent 
years,  and  the  meanings  exactly  fixed  and  maintained 
invariable.  Every  science  has  or  ought  to  have  a  series 


jo  OF  THE  AMBIGUITY  [] 

of  terms  equally  precise  and  certain  in  meaning.  (Set 
Lesson  xxxm.)  The  names  of  individual  objects,  build- 
ings, events,  or  persons,  again,  are  usually  quite  certain 
uid  clear,  as  in  J  ulius  Caesar,  William  the  Conqueror,  the 
irst  Napoleon,  Saint  Peter's,  Westminster  Abbey,  the 
ireat  Exhibition  of  1851,  and  so  on. 

But  however  numerous  may  be  the  univocal  terms 
vhich  can  be  adduced,  still  the  equivocal  terms  are  asto- 
11  shingly  common.  They  include  most  of  the  nouns  and 
idjectives  which  are  in  habitual  use  in  the  ordinary 
intercourse  of  life.  They  are  called  ambiguous  from  the 
Latin  verb  ambigo,  to  wander,  hesitate,  or  be  in  doubt;  or 
.  gain  hontonymousy  from  the  Greek  o^os,  like,  and  OVO/AO, 
name.  Whenever  a  person  uses  equivocal  words  in  such 
a  way  as  to  confuse  the  different  meanings  and  fall  into 
error,  he  may  be  said  to  commit  the  fallacy  of  Equivoca- 
tion in  the  logical  meaning  of  the  name  (see  Lesson  XX.) ; 
but  in  common  life  a  person  is  not  said  to  equivocate 
unless  he  uses  words  consciously  and  deceitfully  in  a 
manner  calculated  to  produce  a  confusion  of  the  true  and 
apparent  meanings. 

I  will  now  describe  the  various  kinds  and  causes  ol 
ambiguity  of  words,  following  to  some  extent  the  inter- 
esting chapters  on  the  subject  in  Dr  Watts'  Logic.  In 
the  first  place  we  may  distinguish  three  classes  of  equi- 
rocal  words,  according  as  they  are — 

1.  Equivocal  in  sound  only. 

2.  Equivocal  in  spelling  only. 

3.  Equivocal  both  in  sound  and  spelling. 

Fhe  first  two  classes  are  comparatively  speaking  of  very 
ilight  importance,  and  do  not  often  give  rise  to  serious 
error.  They  produce  what  we  should  call  trivial  mis- 
takes. Thus  we  may  confuse,  when  spoken  only,  the 
words  right,  wright  and  rite  (ceremony) ;  also  the  wordi 
rein,  rain  and  reign,  might  and  mite,  &c.  Owing  partly 


IV.]  OF  TERMS.  * 

to  defects  of  pronunciation  mistakes  are  not  unknowi 
between  the  four  words  air,  hair,  hare  and  heir. 

Words  equivocal  in  spelling  but  not  in  sound  are  such 
as  tear  (a  drop),  and  tear  pronounced  tare,  meaning  a 
rent  in  cloth  ;  or  lead,  the  metal,  and  lead,  as  in  follow- 
ing the  lead  of  another  person.  As  little  more  than  mo- 
mentary misapprehension,  however,  can  arise  from  such 
resemblance  of  words,  we  shall  pass  at  once  to  the  class 
of  words  equivocal  both  in  sound  and  spelling.  These  I 
shall  separate  into  three  groups  according  as  the  equivo- 
cation  arises — 

i.     From  the  accidental  confusion  of  different  words. 

x     From  the  transfer  of  meaning  by  the  association  of 
ideas. 

3.    From  the  logical  transfer  of  meaning  to  analogous 

objects. 

i.  Under  the  first  class  we  place  a  certain  number 
of  curious  but  hardly  important  cases  in  which  ambi- 
guity has  arisen  from  the  confusion  of  entirely  different 
words,  derived  from  different  languages  or  from  differ- 
ent roots  of  the  same  language,  but  which  have  in 
the  course  of  time  assumed  the  same  sound  and  spell- 
ing. Thus  the  word  mean  denotes  either  that  which 
is  medium  or  mediocre,  from  the  French  moyen  and 
the  Latin  medius,  connected  with  the  Anglo -Saxon 
mid,  or  middle;  or  it  denotes  what  is  low-minded  and 
base,  being  then  derived  from  the  Anglo-Saxon  Gemane, 
which  means  "  that  belonging  to  the  mcene  or  many," 
whatever  in  short  is  vulgar.  The  verb  to  mean  can 
hardly  be  confused  with  the  adjective  mean,  but  it  comes 
from  a  third  distinct  root,  probably  connected  with  the 
Sanscrit  verb,  to  think. 

As  other  instances  of  this  casual  ambiguity,  I  may 
mention  rent,  a  money  payment,  from  the  French  renU 
^  to  return),  or  a  tear,  the  result  of  the  action  o/ 


p  OF   THE    AMBiGUITY  [iXSk 

reiuling,  this  word  being  of  Anglo-Saxon  origin  and  on« 
of  the  numerous  class  beginning  in  r  or  wr,  which  imitate 
more  or  less  perfectly  the  sound  of  the  action  which  the) 
denote.  Pound,  from  the  Latin  pondus,  a  weight,  is  con- 
fused with  pound,  in  the  sense  of  a  village  pinfold  foi 
cattle,  derived  from  the  Saxon  pyndany  to  pen  up.  /»>//, 
a  mountain,  is  a  perfectly  distinct  word  from  fell,  a  skin 
or  hide ;  and  pulse,  a  throb  or  beating,  and  pulse,  peas, 
beans,  or  potage,  though  both  derived  from  the  Greek  or 
Latin,  are  probably  quite  unconnected  words.  It  is 
curious  that  gin,  in  the  meaning  of  trap  or  machine,  is  a 
contracted  form  of  engine,  and  when  denoting  the  spirit- 
uous liquor  is  a  corruption  of  Geneva,  the  place  where  the 
spirit  was  first  made. 

Certain  important  cases  of  confusion  have  been  de- 
tected in  grammar,  as  between  the  numeral  one,  derived 
from  an  Aryan  root,  through  the  Latin  unus,  and  the  in- 
determinate pronoun,  one  (as  in  "one  ought  to  do  one's 
duty"),  which  is  really  a  corrupt  form  of  the  French 
word  homme  or  man.  The  Germans  to  the  present  day 
use  man  in  this  sense,  as  in  man  sagt,  i.e.  one  says. 

2.  By  far  the  largest  part  of  equivocal  words  have 
become  so  by  a  transfer  of  the  manning  from  the  thing 
originally  denoted  by  the  word  to  some  other  thing 
habitually  connected  with  it  so  as  to  become  closely  as- 
sociated in  thought  Thus,  in  Parliamentary  language, 
the  House  means  either  the  chamber  in  which  the  mem- 
bers meet,  or  it  means  the  body  of  members  who  happen 
to  be  assembled  in  it  at  any  time.  Similarly,  the  word 
church  originally  denoted  the  building  (/tvpioicoi/,  the 
Lord's  House)  in  which  any  religious  worshippers  assem- 
ble, but  it  has  thence  derived  a  variety  of  meanings ;  it 
may  mean  a  particular  body  of  worshippers  accustomed 
to  assemble  in  any  one  place,  in  which  sense  it  is  used  in 
4cts  xiv.  23 ;  or  it  means  any  body  of  persons  holding 


iv.]  OF  TERMS.  31 

the  same  opinions  &nd  connected  in  one  organization,  ai 
in  the  Anglican,  or  Greek,  or  Roman  Catholic  Church  j 
it  is  also  sometimes  used  so  as  to  include  the  laity  as  well 
as  the  clergy ;  but  more  generally  perhaps  the  clergy  and 
religious  authorities  of  any  sect  or  country  are  so  strongly 
issociated  with  the  act  of  worship  as  to  be  often  called 
the  church  par  excellence.  It  is  quite  evident  moreover 
that  the  word  entirely  differs  in  meaning  according  as  it 
is  used  by  a  member  of  the  Anglican,  Greth,  Roman 
Catholic,  Scotch  Presbyterian,  or  any  other  existing 
church. 

The  word  foot  has  suffered  several  curious  but  very 
evident  transfers  of  meaning.  Originally  it  denoted  the 
foot  of  a  man  or  an  animal,  and  is  probably  connected  in 
a  remote  manner  with  the  Latin  pes,  pedis,  and  the  Greek 
»ro*;y,  iro86s ',  but  since  the  length  of  the  foot  is  naturally 
employed  as  a  rude  measure  of  length,  it  came  to  be 
applied  to  a  fixed  measure  of  length ;  and  as  the  foot  is 
at  the  bottom  of  the  body  the  name  was  extended  by 
analogy  to  the  foot  of  a  mountain,  or  the  feet  of  a  table  j 
by  a  further  extension,  any  position,  plan,  reason,  or 
argument  on  which  we  place  ourselves  and  rely,  is  called 
the  foot  or  footing.  The  same  word  also  denotes  soldiers 
who  fight  upon  their  feet,  or  infantry,  and  the  measured 
part  of  a  verse  having  a  definite  length.  That  these  very 
different  meanings  are  naturally  connected  with  the  ori- 
ginal meaning  is  evident  from  the  fact  that  the  Latin 
and  Greek  words  for  foot  are  subject  to  exactly  similar 
series  of  ambiguities. 

It  would  be  a  long  task  to  trace  out  completely  the 
various  and  often  contradictory  meanings  of  the  word 
fallow.  Originally  a  fellow  was  whaty&//0«/.r  another,  that 
is  a  companion ;  thus  it  came  to  mean  the  other  of  a  pair, 
as  one  shoe  is  the  fellow  of  the  other,  or  simply  an  equal, 
as  when  we  say  that  Shakspeare  "hath  not  a  fellow/ 


54  OF  THE  AMBIGUITY  [LESS 

From  the  simple  meaning  of  companion  again  it  comes 
U)  denote  vaguely  a  person,  as  in  the  question  "What 
fellow  is  that?"  but  then  there  is  a  curious  confusion  oi 
depreciatory  and  endearing  power  in  the  word ;  when  a 
man  is  called  a  mere  fellow,  or  simply  a  fellow  in  a  par- 
ticular tone  of  voice,  the  name  is  one  of  severe  contempt , 
alter  the  tone  of  voice  01  the  connected  words  in  the  least 
degree,  and  it  becomes  one  of  the  most  sweet  and  en- 
dearing appellations,  as  when  we  speak  of  a  dear  01 
good  fellow.  We  may  still  add  the  technical  meanings  ol 
the  name  as  applied  in  the  case  of  a  Fellow  of  a  College, 
or  of  a  learned  society. 

Another  good  instance  of  the  growth  of  a  number  oi 
different  meanings  from  a  single  root  is  found  in  the 
word  post.  Originally  a  post  was  something  posited,  or 
placed  firmly  in  the  ground,  such  as  an  upright  piece  oi 
wood  or  stone ;  such  meaning  still  remains  in  the  cases 
of  a  lamp-post,  a  gate-post,  signal-post,  &c.  As  a  post 
would  often  be  used  to  mark  a  fixed  spot  of  ground,  as  in 
a  mile-post,  it  came  to  mean  the  fixed  or  appointed  place 
where  the  post  was  placed,  as  in  a  military  post,  the  post 
of  danger  or  honour,  &c.  The  fixed  places  where  horsea 
were  kept  in  readiness  to  facilitate  rapid  travelling  during 
the  times  of  the  Roman  empire  were  thus  called  posts, 
and  thence  the  whole  system  of  arrangement  for  the  con- 
veyance of  persons  or  news  came  to  be  called  the  posts. 
The  name  has  retained  an  exactly  similar  meaning  to  the 
present  day  in  most  parts  of  Europe,  and  we  still  use  it 
in  post-chaise,  post-boy,  post-horse  and  postillion.  A 
system  of  post  conveyance  for  letters  having  been  organ- 
ised for  about  two  centuries  in  England  and  other  coun 
tries,  this  is  perhaps  the  meaning  most  closely  associated 
with  the  word  post  at  present,  and  a  number  of  expres- 
sions have  thus  arisen,  such  as  post-office,  postage,  postal- 
guide,  postman,  postmaster,  postal-telegraph,  &c.  Curi 


IV.]  Of  TERMS.  £ 

oasly  enough  we  now  have  iron  letter-posts,  in  which  th« 
word  post  is  restored  exactly  to  its  original  meaning. 

Although  the  words  described  above  were  selected  on 
account  of  the  curious  variety  of  their  meanings,  I  do  not 
hesitate  to  assert  that  che  majority  of  common  nouns 
possess  various  meanings  in  greater  or  less  number.  Dr 
Watts,  in  his  Logic,  suggests  that  the  words  book,  bible, 
fish,  house,  and  elephant,  are  univocal  terms,  but  the 
reader  would  easily  detect  ambiguities  in  each  of  them, 
Thus  fish  bears  a  very  different  meaning  in  natural  his- 
tory from  what  it  does  in  the  mouths  of  unscientific  per- 
sons, who  include  under  it  not  only  true  fishes,  but  shell- 
fish or  mollusca,  and  the  cetacea,  such  as  whales  and 
seals,  in  short  all  swimming  animals,  whether  they  have 
the  character  of  true  fish  or  not.  Elephant,  in  a  station- 
er's or  bookseller's  shop,  means  a  large  kind  of  paper 
instead  of  a  large  animaL  Bible  sometimes  means  any 
particular  copy  of  the  Bible,  sometimes  the  collection 
of  works  constituting  the  Holy  Scriptures.  The.  word 
man  is  singularly  ambiguous  ;  sometimes  it  denotes  man 
as  distinguished  from  woman;  at  other  times  it  is  cer- 
tainly used  to  include  both  /sexes ;  and  in  certain  recent 
election  cases  lawyers  were  unable  to  decide  whether  the 
word  man  as  used  in  the  Reform  Act  of  1867  ought  or 
ought  not  to  be  interpreted  so  as  to  include  women.  On 
other  occasions  man  is  used  to  denote  an  adult  male  as 
distinguished  from  a  boy,  and  it  also  often  denotes  one 
who  is  emphatically  a  man  as  possessing  a  masculine 
character.  Occasionally  it  is  used  in  the  same  way  as 
groom,  for  a  servant,  as  in  the  proverb,  u  Like  master, 
like  man."  At  other  times  it  stands  specially  tor  a  bus 
band. 

3.  Among  ambiguous  words  we  must  thirdly  distinguish 
those  which  derive  their  various  meanings  in  a  somewhat 
different  manner,  namely  by  analogy  or  real  resemblance 


j6         THE  AMBIGUITY  OF  TERMS.      [LESS,  n 

When  we  speak  of  a  sweet  taste,  a  sweet  flower,  a  swee» 
tune,  a  sweet  landscape,  a  sweet  face,  a  sweet  poem,  it  is 
evident  that  we  apply  one  and  the  same  word  to  very 
different  things ;  such  a  concrete  thing  as  lump-sugar  can 
hardly  be  compared  directly  with  such  an  intellectual 
existence  as  Tennyson's  May  Queen.  Nevertheless  if  the 
word  sweet  is  to  be  considered  ambiguous,  it  is  in  a  dif- 
ferent way  from  those  we  have  before  considered,  because 
all  the  things  are  called  sweet  on  account  of  a  peculiar 
pleasure  which  they  yield,  which  cannot  be  desciibed 
otherwise  than  by  comparison  with  sugar.  In  a  similai 
way,  we  describe  a  pain  as  sharp,  a  disappointment  as 
bitter,  a  person's  temper  as  sour,  the  future  as  bright  or 
gloomy,  an  achievement  as  brilliant ;  all  these  adjectives 
implying  comparison  with  bodily  sensations  of  the  sim- 
plest kind.  The  adjective  brilliant  is  derived  from  the 
French  briller,  to  glitter  or  sparkle ;  and  this  meaning  it 
fully  retains  when  we  speak  of  a  brilliant  diamond,  a 
brilliant  star,  &c.  By  what  a  subtle  analogy  is  it  that  we 
speak  of  a  brilliant  position,  a  brilliant  achievement, 
brilliant  talents,  brilliant  style !  We  cannot  speak  of  a 
clear  explanation,  indefatigable  perseverance,  perspicuous 
style,  or  sore  calamity,  without  employing  in  each  of  these 
expressions  a  double  analogy  to  physical  impressions, 
actions,  or  events.  It  will  be  shewn  in  the  sixth  Lesson 
that  to  this  process  we  owe  the  creation  of  all  names 
connected  with  mental  feelings  or  existences. 

Read  Watts'  Logic,  Chapter  iv. 

Locke's  Essay  on  tJu  Human  Understanding,  Book  III 
Chapters  ix.  and  X. 


LESSON  V. 

Qf  THE  TWOFOLD    MEANING   OF   TERMS-. 
IN   EXTENSION   AND   INTENSION. 

THERE  is  no  part  of  the  doctrines  of  Logic  to  which  I 
would  more  urgently  request  the  attention  of  the  reader 
than  to  that  which  I  will  endeavour  to  explain  clearly  in 
the  present  Lesson.  I  speak  of  the  double  meaning 
which  is  possessed  by  most  logical  terms — the  meaning 
in  extension,  and  the  meaning  in  Intension.  I  believe 
that  the  reader  who  once  acquires  a  thorough  apprehen- 
sion of  the  difference  of  these  meanings,  and  learns  to 
bear  it  always  in  mind,  will  experience  but  little  further 
difficulty  in  the  study  of  logic. 

The  meaning  of  a  term  in  extension  consists  of  the 
objects  to  which  the  term  may  be  applied ;  its  meaning  in 
intension  consists  of  the  qualities  which  are  necessarily 
possessed  by  objects  bearing  that  name.  A  simple  example 
will  make  this  distinction  most  apparent  What  is  the 
meaning  of  the  name  "metal"?  The  first  and  most  ob- 
vious answer  is  that  metal  means  either  gold,  or  silver,  or 
iron,  or  copper,  or  aluminium,  or  some  other  of  the  48 
substances  known  to  chemists,  and  considered  to  have  a 
metallic  nature.  These  substances  then  form  the  plain 
and  common  meaning  of  the  name,  which  is  the  meaning 
in  extension.  But  if  it  be  asked  why  the  name  is  applied 
to  all  these  substances  and  these  only,  the  answer  must 
be — Because  they  possess  certain  qualities  which  belong 
to  the  nature  of  metal.  We  cannot,  therefore,  know  to 
what  substances  we  may  apply  the  name,  or  to  what  we 


38     I  WOFOLD  MEANING  OF  TERMS— 

may  not,  unless  we  know  the  qualities  which  are  indis- 
pensable to  the  character  of  a  metal  Now  chemists  lay 
these  down  to  be  somewhat  as  follows: — (i)  A  metal 
must  be  an  element  or  simple  substance  incapable  ol 
decomposition  or  separation  into  simpler  substances  by 
any  known  means.  (2)  It  must  be  a  good  conductor  ol 
heat  and  electricity.  (3)  It  must  possess  a  great  and 
peculiar  reflective  power  known  as  metallic  lustre*. 

These  properties  are  common  to  all  metals,  or  nearly 
all  metals,  and  are  what  mark  out  and  distinguish  a 
metal  from  other  substances.  Hence  they  form  in  a 
certain  way  the  meaning  of  the  name  metal,  the  meaning 
in  intension,  as  it  is  called,  to  distinguish  it  from  the 
former  kind  of  meaning. 

In  a  similar  manner  almost  any  other  common  name 
has  a  double  meaning.  "Steamship"  denotes  in  exten- 
sion the  Great  Eastern,  the  Persia,  the  Himalaya,  or  any 
one  of  the  thousands  of  steamships  existing  or  which 
have  existed;  in  intension  it  means  "a  vessel  propelled 
by  steam-power."  Monarch  is  the  name  of  Queen  Vic- 
toria, Victor  Emmanuel,  Louis  Napoleon,  or  any  one  of  a 
considerable  number  of  persons  who  rule  singly  over 
countries;  the  persons  themselves  form  the  meaning  in 
extension ;  the  quality  of  ruling  alone  forms  the  intensive 
meaning  of  the  name.  Animal  is  the  name  in  extension 
of  any  one  of  billions  of  existing  creatures  and  of  indefi 
nitely  greater  numbers  of  other  creatures  that  have  ex 
isted  or  will  exist ;  in  intension  it  implies  in  all  those 
creatures  the  existence  of  a  certain  animal  life  and  sense, 
or  at  least  the  power  of  digesting  food  and  exerting  force, 
which  are  the  marks  of  animal  nature. 

*  It  is  doubtfully  true  that  all  metals  possess  metallic  lustre, 
and  chemists  would  find  it  very  difhcult  to  give  any  consistent 
explanation  of  their  use  of  the  name  ;  bat  the  statements  in  thf 
tort  are  sufficiently  true  to  furnish  an  example. 


V.]        IN  EXTENSION  AND  INTENSION.       3^ 

It  is  desirable  to  state  here  that  this  distinction  ol 
extension  and  intension  has  been  explained  by  logi- 
cians under  various  forms  of  expression.  It  is  the  pe- 
culiar misfortune  of  the  science  of  logic  to  have  a  super* 
fluity  of  names  or  synonyms  for  the  same  idea.  Thus  the 
intension  of  a  term  is  synonymous  with  its  comprehen- 
ilon,  or  connotation,  or  depth;  while  the  extension  is 
synonymous  with  the  denotation  or  breadth.  This  may 
be  most  clearly  stated  in  the  form  of  a  scheme: — 

The  extension,  extent,          /he     intension,     intent, 

breadth,    denotation,    do-  depth,  connotation,  or   im- 

main,  sphere  or  application  plication    of  a    name    con-> 

of  a  name  consists  of  the  sists    of    the    qualities    the 

individual  things  to  which  possession  of  which  by  those 

the  name  applies.  things  is  implied. 

Of  these  words,  denotation  and  connotation  are  employed 
chiefly  by  Mr  J.  S.  Mill  among  modern  logical  writers, 
and  are  very  apt  for  the  purpose.  To  denote  is  to  mark 
down,  and  the  name  marks  the  things  to  which  it  may  be 
applied  or  affixed;  thus  metal  denotes  gold,  silver,  cop- 
per, Sec.  To  connote  is  to  mark  along  with  (Latin  con, 
together;  notare,  to  mark),  and  the  connotation  accord- 
ingly consists  of  the  qualities  before  described,  the  pos- 
session of  which  is  implied  by  the  use  of  the  name  metaL 
When  we  compare  different  but  related  terms  we  may 
observe  that  they  differ  in  the  quantity  of  their  extension 
and  intensioa  Thus  the  term  element  has  a  greater 
extension  of  meaning  than  metal,  because  it  includes  in 
its  meaning  all  metals  and  other  substances  as  well 
But  it  has  at  the  same  time  less  intension  of  meaning; 
for  among  the  qualities  of  a  metallic  substance  must  be 
found  the  qualities  of  an  element,  besides  the  othei 
qualities  peculiar  to  a  metal.  If  again  we  compare  the 
terms  metal  and  malleable  metal,  it  is  apparent  fhat  tht 


40     TWOFOLD  MEANING  OF  TERMS—    [LESi 

latter  term  does  not  include  the  metals  antimony,  arsenic 
and  bismuth,  which  are  brittle  substances.  Hence  mal- 
leable metal  is  a  term  of  narrower  meaning  in  extension 
than  metal ;  but  it  has  also  deeper  meaning  in  intension, 
because  it  connotes  or  implies  the  quality  of  malleability 
in  addition  to  the  general  qualities  of  a  metal  WhiU 
malleable  metal  is  again  a  narrower  term  in  extension 
because  it  does  not  include  gold  and  copper ;  and  I  can 
go  on  narrowing  the  meaning  by  the  use  of  qualifying  ad- 
jectives until  only  a  single  metal  should  be  denoted  by 
the  term. 

The  reader  will  now  see  clearly  that  a  general  law  of 
great  importance  connects  the  quantity  of  extension  and 
the  quantity  of  intension,  viz. — As  the  intension  of  a  term 
IB  Increased  the  extension  is  decreased.  It  must  not  be 
supposed,  indeed,  that  there  is  any  exact  proportion  be- 
tween the  degree  in  which  one  meaning  is  increased  and 
the  other  decreased.  Thus  if  we  join  the  adjective  red  to 
metal  we  narrow  the  meaning  much  more  than  if  we  join 
the  adjective  white,  for  there  are  at  least  twelve  times 
as  many  white  metals  as  red.  Again,  the  term  white 
man  includes  a  considerable  fraction  of  the  meaning  of 
the  term  man  as  regards  extension,  but  the  term  blind 
man  only  a  small  fraction  of  the  meaning.  Thus  it  is 
obvious  that  in  increasing  the  intension  of  a  terra  we  ma) 
decrease  the  extension  in  any  degree. 

In  understanding  this  law  we  must  carefully  discrimi- 
nate the  cases  where  there  is  only  an  apparent  increase  of 
the  intension  of  a  term,  from  those  where  the  increase  is 
real  If  I  add  the  term  elementary  to  metal^  I  shall  not 
really  alter  the  extension  of  meaning,  for  all  the  metals 
are  elements;  and  the  elementary  metals  are  neither 
more  nor  less  numerous  than  the  metals.  But  then  the 
intension  of  the  term  is  really  unaltered  at  the  same  time  ; 
for  the  quality  of  an  element  is  really  found  among  thf 


v.j        IN  EXTENSION  AND  INTENSION.      4* 

qualities  of  metal,  and  it  is  superfluous  to  specify  it  ovei 
again.  A  quality  which  belongs  invariably  to  the  whole 
of  a  class  of  things  is  commonly  called  a  property  of  the 
class  (see  Lesson  xn.),  and  we  cannot  qualify  or  restrict 
a  term  by  its  own  property. 

This  is  a  convenient  place  to  notice  a  distinction  be- 
cween  terms  into  those  which  are  connotative  and  those 
which  are  non-connotative,  the  latter  consisting  of  the 
terms  which  simply  denote  things  without  implying  any 
knowledge  of  their  qualities.  As  Mr  Mill  considers  this 
distinction  to  be  one  of  great  importance,  it  will  be  well 
to  quote  his  own  words*: — 

"  A  non-connotative  term  is  one  which  signifies  a  sub- 
ject only,  or  an  attribute  only.  A  connotative  term  is 
one  which  denotes  a  subject,  and  implies  an  attribute. 
By  a  subject  is  here  meant  anything  which  possesses 
attributes.  Thus  John,  or  London,  or  England,  are 
names  which  signify  a  subject  only.  Whiteness,  length, 
virtue,  signify  an  attribute  only.  None  of  these  names, 
therefore,  are  connotative.  But  white,  long,  virtuous, 
are  connotative.  The  word  white  denotes  all  white 
things,  as  snow,  paper,  the  foam  of  the  sea,  &c.,  and 
implies,  or,  as^it  was  termed  by  the  schoolmen,  connotes 
the  attribute  whiteness.  The  word  white  is  not  predi- 
cated of  the  attribute,  but  of  the  subjects,  snow,  &c. ;  but 
when  we  predicate  it  of  them,  we  imply,  or  connote,  that 
the  attribute  whiteness  belongs  to  them 

"All  concrete  general  names  are  connotative.  The 
word  man,  for  example,  denotes  Peter,  James,  John,  and 
an  indefinite  number  of  other  individuals,  of  whom,  taken 
as  a  class,  it  is  the  name.  But  it  is  applied  to  them,  be* 
cause  they  possess,  and  to  signify  that  they  possess,  cer- 

w  System  of  Logic ;  Vol.  I.  p.  31,  6th  ed.  Book  L  Chap.  II 
IS 


43       TWOFOLD  MEANING  OF  TERMS—  [LESS 

fain  attributes. . . .  What  we  call  men,  are  the  subjects, 
the  individual  Styles  and  Nokes ;  not  the  qualities  by 
which  their  humanity  is  constituted.  The  name  therefore 
is  said  to  signify  the  subjects  directly,  the  attributes  to- 
directly ;  it  denotes  the  subjects,  and  implies,  or  involves 
or  indicates,  or,  as  we  shall  say  henceforth,  connotes,  the 
Attributes,  It  is  a  connotative  name  .... 

"  Proper  names  are  not  connotative  :  they  denote  the 
individuals  who  are  called  by  them ;  but  they  do  not  indi- 
cate or  imply  any  attributes  as  belonging  to  those  indivi- 
duals. When  we  name  a  child  by  the  name  Paul,  or  a  dog 
by  the  name  Caesar,  these  names  are  simply  marks  used 
to  enable  those  individuals  to  be  made  subjects  of  dis- 
course. It  may  be  said,  indeed,  that  we  must  have  had 
some  reason  for  giving  them  those  names  rather  than 
any  others  ;  and  this  is  true  ;  but  the  name,  once  given,  is 
independent  of  the  reason.  A  man  may  have  been  named 
John,  because  that  was  the  name  of  his  father ;  a  town 
may  have  been  named  Dartmouth,  because  it  is  situ- 
ated at  the  mouth  of  the  Dart.  But  it  is  no  part  of  the 
signification  of  the  word  John,  that  the  father  of  the  per- 
son so  called  bore  the  same  name ;  nor  even  of  the  word 
Dartmouth  to  be  situated  at  the  mouth  of  the  Dart.  If 
sand  should  choke  up  the  mouth  of  the  river,  or  an  earth 
quake  change  its  course,  and  remove  it  to  a  distance  from 
the  town,  the  name  of  the  town  would  not  necessarily  be 
changed." 

I  quote  this  in  Mr  Mill's  own  words,  because  though 
it  expresses  most  clearly  the  view  accepted  by  Mr  Mill 
and  many  others,  it  is  nevertheless  probably  erroneous. 
The  connotation  of  a  name  is  confused  with  the  etymo- 
kogical  meaning,  or  the  circumstances  which  caused  it  to 
be  affixed  to  a  thing.  Surely  no  one  who  uses  the  name 
England,  and  knows  what  it  denotes,  can  be  ignorant  of 
the  peculiar  qualities  and  circumstances  of  the  country, 


v  ]        IN  EXTENSION  AND  INTENSION.     4m 

and  these  form  the  connotation  of  the  term.  To  any  one 
who  knows  the  town  Dartmouth  the  name  must  imply  ths 
possession  of  the  circumstances  by  which  that  town  is  cha- 
racterised at  the  present  time.  If  the  river  Dart  should  b< 
destroyed  or  removed,  the  town  would  so  far  be  altered, 
and  the  signification  of  the  name  changed.  The  name 
urould  no  longer  denote  a  town  situated  on  the  Dart,  but 
one  which  was  formerly  situated  on  the  Dart,  and  it  would 
be  by  a  mere  historical  accident  that  the  form  of  the  name 
did  not  appear  suitable  to  the  town.  So  again  any  proper 
dame  such  as  John  Smith,  is  almost  without  meaning  until 
we  know  the  John  Smith  in  question.  It  is  true  that  the 
name  alone  connotes  the  fact  that  he  is  a  Teuton,  and 
is  a  male ;  but,  so  soon  as  we  know  the  exact  individual 
it  denotes,  the  name  surely  implies,  also,  the  peculiar  fea- 
tures, form,  and  character,  of  that  individual  In  fact,  as 
it  is  only  by  the  peculiar  qualities,  features,  or  circum- 
stances of  a  thing,  that  we  can  ever  recognise  it,  no  name 
could  have  any  fixed  meaning  unless  we  attached  to  it, 
mentally  at  least,  such  a  definition  of  the  kind  of  thing 
denoted  by  it,  that  we  should  know  whether  any  given 
thing  was  denoted  by  it  or  not.  If  the  name  John  Smith 
does  not  suggest  to  my  mind  the  qualities  of  John  Smith, 
how  shall  I  know  him  when  I  meet  him?  for  he  certainly 
does  not  bear  his  name  written  upon  his  brow  *. 

This,  however,  is  quite  an  undecided  question;  and 
as  Mr  Mill  is  generally  considered  the  best  authority  upon 
the  subject,  it  may  be  well  for  the  reader  provisionally  to 
accept  his  opinion,  that  singular  or  proper  names  are 
con  -connotative,  and  all  concrete  general  names  are  con- 
rotative.  Abstract  names,  on  the  other  hand,  can  hardly 

*  Further  objections  to  Mr  Mill's  views  on  this  point  will 
be  found  in  Mr  Shedden's  Elements  if  Logic.  London,  1864 
pp.  H,  &c. 


44  TWOFOLD  MEANING  OF  TERMS.  [LESi 
possess  connotation  at  all,  for  as  they  already  denote  thi 
attributes  or  qualities  of  something,  there  is  nothing  left 
which  can  form  the  connotation  of  the  name.  Mr  Mill, 
indeed,  thinks  that  abstract  names  may  often  be  consi- 
dered connotative,  as  when  the  name  fault  connotes  the 
attribute  of  hurtfulness  as  belonging  to  fault.  But  if 
fault  is  a  true  abstract  word  at  all  I  should  regard  hurt 
fulness  as  a  part  of  its  denotation  ;  I  am  inclined  to  think 
that  faultiness  is  the  abstract  name,  and  that  fault  is  gene- 
rally used  concretely  as  the  name  of  a  particular  action  or 
thing  that  is  faulty,  or  possesses  faultiness.  But  the  sub- 
ject cannot  be  properly  discussed  here,  and  the  reader 
snould  note  Mr  Mill's  opinion  that  abstract  names  are 
usually  non-connotative,  but  may  be  connotative  in  some 
cases. 

The  subject  of  Extension  and  Intension  may  be  pur- 
sued in  Hamilton's  Lectures  on  Logic,  Lect  VIIL  j 
or  in  Thomson's  Laws  of  Thought,  Sections  48  to 
52.  It  is  much  noticed  in  Spalding's  Logic  (Ency- 
clopaedia Britannica,  8th 


^io!^> 


LESSON  VI. 
THE  GROWTH   OF  LANGUAGE. 

WORDS,  we  have  seen,  become  equivocal  in  at  least  three 
different  ways — by  the  accidental  confusion  of  different 
words,  by  the  change  of  meaning  of  a  word  by  iti 
habitual  association  with  other  things  than  its  original 
meaning,  and  by  analogical  transfer  to  objects  of  a  similai 
nature.  We  must  however  consider  somewhat  more 
:k>«ely  certain  changes  in  language  which  arise  out  of  thf 


7WE1  GROWTH  OF  LANGUAGE.          45 

last  cause,  and  which  are  in  constant  progress.  We  can 
almost  trace  in  fact  the  way  in  which  language  is  created 
and  extended,  and  the  subject  is  to  the  logician  one  of  a 
highly  instructive  and  important  character.  There  are 
two  great  and  contrary  processes  which  modify  language 
*s  follows: — 

1.  Generalisation,   by  which   a  name  comes    to  be 
applied  to  a  wider  class  of  objects  than  before,  so  thai 
the  extension  of  its  meaning  is  increased,  and  the  inten- 
sion diminished. 

2.  Specialisation,  by  which  a  name  comes  to  be  re- 
stricted to  a  narrower  class,  the  extension  being  decrease** 
and  the  intension  increased. 

The  first  change  arises  in  the  most  obvious  manner, 
from  our  detecting  a  resemblance  between  a  new  object, 
which  is  without  a  name,  and  some  well-known  object 
To  express  the  resemblance  we  are  instinctively  led  to 
apply  the  old  name  to  the  new  object.  Thus  we  are  well 
acquainted  with  ^/ajj,  and,  if  we  meet  any  substance 
having  the  same  glassy  nature  and  appearance,  we  shall  be 
apt  at  once  to  call  it  a  kind  of  glass ;  should  we  often  meet 
with  this  new  kind  of  glass  it  would  probably  come  to  share 
the  name  equally  with  the  old  and  original  kind  of  glass. 
The  word  coal  has  undergone  a  change  of  this  kind ;  ori- 
ginally it  was  the  name  of  charked  or  charred  wood,  which 
was  the  principal  kind  of  fuel  used  five  hundred  years  ago. 
As  mineral  coal  came  into  use  it  took  the  name  from  the 
former  fuel,  which  it  resembled  more  nearly  than  any- 
thing else,  but  was  at  first  distinguished  as  sea-coal  or 
pit-coal.  Being  now  far  the  more  common  of  the  two,  it 
has  taken  the  simple  name,  and  we  distinguish  charred 
wood  as  charcoal,  Paper  has  undergone  a  like  change  ; 
originally  denoting  the  papyrus  used  in  the  Roman  Em- 
pire, it  was  transferred  to  the  new  writing  material  made 
of  cotton  or  linen  rags,  which  was  introduced  at  a  quit* 


46  THE  GROWTH  OF  LANGUAGE.     [LESS 

uncertain  period.  The  word  character  is  interesting  OB 
account  of  its  logical  employment ;  the  Greek  xaP€LKT^f 
denoted  strictly  a  tool  for  engraving,  but  it  became  trans- 
ferred by  association  to  the  marks  or  letters  engraved 
with  it,  and  this  meaning  is  still  retained  by  the  word  when 
we  speak  of  Greek  characters,  Arabic  characters,  i.  e.  figures 
IT  letters.  But  inasmuch  as  objects  often  have  natural 
marks,  signs>  or  tokens,  which  may  indicate  them  as  well 
as  artificial  characters,  the  name  was  generalized,  and  now 
means  any  peculiar  or  distinctive  mark  or  quality  by  which 
an  object  is  easily  recognised. 

Changes  of  this  kind  are  usually  effected  by  no  parti- 
cular person  and  with  no  distinct  purpose,  but  by  a  sort 
of  unconscious  instinct  in  a  number  of  persons  using  the 
name.  In  the  language  of  science,  however,  changes  are 
often  made  purposely,  and  with  a  clear  apprehension  of 
the  generalization  implied.  Thus  soap  in  ordinary  life 
is  applied  only  to  a  compound  of  soda  or  potash  with 
fat ;  but  chemists  have  purposely  extended  the  name 
so  as  to  include  any  compound  of  a  metallic  salt  with  a 
fatty  substance.  Accordingly  there  are  such  things  as 
lime-soap  and  lead-soap,  which  latter  is  employed  in 
making  common  diachylon  plaster.  Alcohol  at  first  de- 
noted the  product  of  ordinary  fermentation  commonly 
called  spirits  of  wine,  but  chemists  having  discovered  that 
many  other  substances  had  a  theoretical  composition 
closely  resembling  spirits  of  wine,  the  name  was  adopted 
for  the  whole  class,  and  a  long  enumeration  of  different 
kinds  of  alcohols  will  be  found  in  Dr  Roscoe's  lessons 
on  chemistry.  The  number  of  known  alcohols  is  likewis« 
subject  to  indefinite  increase  by  the  progress  of  discovery. 
Every  one  of  the  chemical  terms  acid,  alkali,  metal,  alloy, 
earth,  ether,  oil,  gas,  salt,  may  be  shown  to  have  under- 
gone great  generalizations. 

In  other  sciences  there  is  hardly  a  less  supply  of 


VI.]         THE   GROWTH  OF  LANGUAGE.  45 

instances.  A  lens  originally  meant  a  lenticular  shaped 
or  double  convex  piece  of  glass,  that  being  the  kind  oJ 
glass  most  frequently  used  by  opticians.  But  as  glasses 
of  other  shapes  came  to  be  used  along  with  lenses,  the 
name  was  extended  to  concave  or  even  to  perfectly  flat 
pieces  of  glass.  The  words  lever,  plane,  cone,  cylinder, 
arc,  conic  section,  curve,  prism,  magnet,  pendulum,  ray, 
light,  and  many  others,  have  been  similarly  generalized* 

In  common  language  we  may  observe  that  even 
proper  or  singular  names  are  often  generalized,  as  when 
in  the  time  of  Cicero  a  good  actor  was  called  a  Roscius 
after  an  acior  of  preeminent  talent.  The  name  Caesar 
was  adopted  by  the  successor  of  Julius  Caesar  as  an  official 
name  of  the  Emperor,  with  which  it  gradually  became 
synonymous,  so  that  in  the  present  day  the  Kaisers  of 
Austria  and  the  Czars  of  Russia  both  take  their  title  from 
Caesar.  Even  the  abstract  name  Caesarism  has  been 
formed  to  express  a  kind  of  imperial  system  as  established 
by  Caesar.  The  celebrated  tower  built  by  a  king  of 
Egypt  on  the  island  of  Pharos,  at  the  entrance  of  the 
harbour  of  Alexandria,  has  caused  lighthouses  to  be  called 
phares  in  French,  and  pharos  in  obsolete  English.  From 
the  celebrated  Roman  General  Quintus  Fabius  Maximus 
any  one  who  avoids  bringing  a  contest  to  a  crisis  is  said 
to  pursue  a  Fabian  policy. 

In  science  also  singular  names  are  often  extended,  as 
when  the  fixed  stars  are  called  distant  suns,  or  the  com- 
panions of  Jupiter  are  called  his  moons.  It  is  indeed  one 
theory,  and  a  probable  one,  that  all  general  names  were 
created  by  the  process  of  generalization  going  on  in  the 
early  ages  of  human  progress.  As  the  comprehension  of 
general  notions  requires  higher  intellect  than  the  appre- 
hension of  singular  and  concrete  things,  it  seems  natural 
that  names  should  at  first  denote  individual  objects,  and 
ihould  afterwards  be  extended  to  classes.  We  have  a 


48  THE  GROWTH  Ofr   LANGUAGE. 

glimpse  of  this  process  in  the  case  of  the  Australian  native 
who  had  been  accustomed  to  call  a  large  dog  Cadli,  but 
when  horses  were  first  introduced  into  the  country  they 
adopted  this  name  as  the  nearest  description  of  a  horse 
A  very  similar  incident  is  related  by  Captain  Cook  of  the 
natives  of  Otaheite.  It  may  be  objected,  however,  that  a 
certain  process  of  judgment  must  have  been  exerted  before 
the  suitability  of  a  name  to  a  particular  thing  could  have 
been  perceived,  and  it  may  be  considered  probable  that 
specialization  as  well  as  generalization  must  have  acted 
in  the  earliest  origin  of  language  much  as  it  does  at 
present. 

Specialization  is  an  exactly  opposite  process  to  gene 
ralization  and  is  almost  equally  important  It  consists  in 
narrowing  the  extension  of  meaning  of  a  general  name,  so 
that  it  comes  to  be  the  name  only  of  an  individual  or  a 
minor  part  of  the  original  class.  It  is  thus  we  are  fur- 
nished with  the  requisite  names  for  a  multitude  of  new 
implements,  occupations  and  ideas  with  which  we  deal  in 
advancing  civilization.  The  name  physician  is  derived 
from  the  Greek  <£vo-i  »»  natural,  and  <j)vo-is,  nature,  so  that 
it  properly  means  one  who  has  studied  nature,  especially 
the  nature  of  the  human  body.  It  has  become  restricted, 
however,  to  those  who  use  this  knowledge  for  medical 
purposes,  and  the  investigators  of  natural  science  have 
been  obliged  to  adopt  the  new  rmaxt  physicist.  The  name 
naturalist  has  been  similarly  restricted  to  those  who  study 
animated  nature.  The  name  surgeon  originally  meant 
handicraftsman,  being  a  corruption  of  chirurgeon,  derived 
from  the  Greek  x*tpovpy6s,  hand-worker.  It  has  long  been 
specialized  however  to  those  who  perform  the  mechanical 
parts  of  the  sanatory  art. 

Language  abounds  with  equally  good  examples.  Min- 
ister originally  meant  a  servant,  or  one  who  acted  as  a 
minor  of  another.  Now  it  often  means  specially  the  most 


FL]         THE   GROWTH  OF  LANGUAGE.  4$ 

important  man  in  the  kingdom.  A  chancellor  was  a  clerk 
or  even  a  door-keeper  who  sat  in  a  place  separated  by 
bars  or  cancelli  in  the  offices  of  the  Roman  Emperor's 
palace ;  now  it  is  always  the  name  of  a  high  or  even  the 
highest  dignitary.  Peer  was  an  equal  (Latin,  Par),  and 
we  still  speak  of  being  tried  by  our  peers  ;  but  now,  by  the 
strange  accidents  of  language,  it  means  the  few  who  are 
superior  to  the  rest  of  the  Queen's  subjects  in  rank. 
Deacon,  Bishop,  Clerk,  Queen,  Captain,  General,  are  all 
words  which  have  undergone  a  like  process  of  specializa- 
tion. In  such  words  as  telegraph,  rail,  signal,  station, 
and  many  words  relating  to  new  inventions,  we  may 
trace  the  progress  of  change  in  a  lifetime. 

One  effect  of  this  process  of  specialization  is  very  soon 
to  create  a  difference  between  any  two  words  which  happen 
from  some  reason  to  be  synonymous.  Two  or  more  words 
are  said  to  be  synonymous  (from  the  Greek  <rvv,  with,  and 
ovofia,  name)  when  they  have  the  same  meaning,  as  in  the 
case,  perhaps,  of  teacher  and  instructor,  similarity  and 
resemblance,  beginning  and  commencement,  sameness 
and  identity,  hypothesis  and  supposition,  intension  and 
comprehension.  But  the  fact  is  that  words  commonly 
called  synonymous  are  seldom  perfectly  so,  and  there  are 
almost  always  shades  of  difference  in  meaning  or  use, 
which  are  explained  in  such  works  as  Crabb's  English 
Synonyms.  A  process  called  by  Coleridge  desynonymi- 
sation,  and  by  Herbert  Spencer  differentiation,  is  alwayi 
going  on,  which  tends  to  specialize  one  of  a  pair  of 
synonymous  words  to  one  meaning  and  the  other  to 
mother.  Thus  wave  and  billow  originally  meant  exactly 
he  same  physical  effect,  but  poets  have  now  appropriated 
:he  word  'billow,'  whereas  wave  is  used  chiefly  in  practical 
«id  scientific  matters.  Undulation  is  a  third  synonym, 
which  will  probably  become  the  sole  scientific  term  for 
9  wave  in  course  of  time  Cab  was  originally  a 


$o          THE  GROWTH  OF  LANGUAGE.     |L 

abbreviation  of  cabriolet,  arid  therefore  of  similar  meaning, 
but  it  is  now  specialized  to  mean  almost  exclusively  * 
hackney  cab.  In  America  car  is  becoming  restricted  to 
the  meaning  of  a  railway  car. 

It  may  be  remarked  that  it  is  a  logical  defect  in  ? 
language  to  possess  a  great  number  of  synonymous  terras, 
•ince  we  acquire  the  habit  of  using  them  indifferently 
irithout  being  sure  that  they  are  not  subject  to  ambiguities 
and  obscure  differences  of  meaning.  The  English  lan- 
guage is  especially  subject  to  the  inconvenience  of  having 
a  complete  series  of  words  derived  from  Greek  or  Latin 
roots  nearly  synonymous  with  other  words  of  Saxon  or 
French  origin.  The  same  statement  may,  in  fact,  be 
put  into  Saxon  or  classical  English  •  and  we  often,  as 
Whatdy  has  well  remarked,  seem  to  prove  a  state- 
ment by  merely  reproducing  it  in  altered  language.  The 
rhetorical  power  of  the  language  may  be  increased  by  the 
copiousness  and  variety  of  diction,  but  pitfalls  are  thus 
prepared  for  all  kinds  of  fallacies.  (See  Lessons  XX 
and  xxi.) 

In  addition  to  the  effects  of  generalization  and  speci- 
alization, vast  additions  and  changes  are  made  in  lan- 
guage by  the  process  of  analogous  or  metaphorical  exten- 
sion of  the  meaning  of  words.  This  change  may  be  said, 
no  doubt,  to  consist  in  generalization,  since  there  must 
always  be  a  resemblance  between  the  new  and  old  appli- 
cations of  the  term.  But  the  resemblance  is  often  one  oi 
a  most  distant  and  obscure  kind,  such  as  we  should  call 
analogy  rather  than  identity.  All  words  used  mctapho 
rically,  or  as  similitudes,  are  cases  of  thi«  process  of  ex 
tension.  The  name  metaphor  is  derived  from  the  G  ek 
words  fKra,  over,  and  iptpav,  to  carry ;  and  expresses  ap- 
parently the  transference  of  a  word  from  its  ordinary  to  a 
peculiar  purpose.  Thus  the  old  similitude  of  a  ruler  to 
the  pilot  of  the  vessel  gives  rise  to  many  metaphors  as 


ft]         THE  GROWTH  OF  LANGUAGE  |l 

In  speaking  of  the  Prime  Minister  being  at  the  Helm  o< 
the  State.  The  word  governor,  and  all  its  derivatives,  is, 
in  fact,  one  result  of  this  metaphor,  being  merely  a  corrupt 
form  of  gubernator,  steersman.  The  words  compass,  pole 
Itar,  ensign,  anchor,  and  many  others  connected  with  na- 
rigation,  are  constantly  used  in  a  metaphorical  manner. 
Prom  the  use  of  horses  and  hunting  we  derive  another 
>et  of  metaphors ;  as,  in  taking  the  reins  of  government, 
overturning  the  government,  taking  the  bit  between  the 
teeth,  the  Government  Whip,  being  heavily  weighted,  &c. 
No  doubt  it  might  be  shewn  that  every  other  important 
occupation  of  life  has  furnished  its  corresponding  stock 
of  metaphors. 

It  is  easy  to  shew,  however,  that  this  process,  besides 
going  on  consciously  at  the  present  day,  must  have  acted 
throughout  the  history  of  language,  and  that  we  owe  to 
it  almost  all,  or  probably  all,  the  words  expressive  of  re- 
fined mental  or  spiritual  ideas.  The  very  word  spirit,  now 
the  most  refined  and  immaterial  of  ideas,  is  but  the  Latin 
spiritus,  a  gentle  breeze  or  breathing;  and  inspiration, 
esprit,  or  wit,  and  many  other  words,  are  due  to  this  me- 
taphor. It  is  truly  curious,  however,  that  almost  all  the 
words  in  different  languages  denoting  mind  or  soul  imply 
the  same  analogy  to  breath.  Thus,  soul  is  from  the 
Gothic  root  denoting  a  strong  wind  or  storm ;  the  Latin 
words  animus  and  anima  are  supposed  to  be  connected 
with  the  Greek  avffju>s,  wind;  ^X1?  *s  certainly  derived 
from  V™*«» to  olow  5  *nw/*a,  ^  or  breath,  is  used  in  the 
New  Testament  for  Spiritual  Being  ;  and  our  word  ghost 
has  been  asserted  to  have  a  similar  origin. 

Almost  all  the  terms  employed  in  mental  philosophy 
>r  metaphysics,  to  denote  actions  or  phenomena  of  mind, 
are  ultimately  derived  from  metaphors.  Apprehension  is 
the  putting  forward  of  the  hand  to  take  anything ;  com- 
prehension  is  the  taking  of  things  together  in  a  handful 

4—2 


fa  THE  GROWTH  OF  LANGUAGE.     [LVS\ 

extension  is  the  spreading  out;  intention,  the  bending  to-, 
-xplication,  the  unfolding;  application,  the  folding  toj 
conception,  the  taking  up  together ;  relation,  the  carrying 
back ;  experience  is  the  thoroughly  going  through  a  thing ; 
difference  is  the  carrying  apart ;  deliberation,  the  weighing 
out ;  interruption,  the  breaking  between ;  proposition,  the 
placing  before;  intuition,  the  seeing  into;  and  the  list 
might  be  almost  indefinitely  extended.  Our  English 
iiame  for  reason,  the  understanding,  obviously  contains 
some  physical  metaphor  which  has  not  been  fully  ex- 
plained ;  with  the  Latin  intellect  there  is  also  a  metaphor. 

Every  sense  gives  rise  to  words  of  refined  meaning ; 
sapience,  taste,  insipidity,  gout,  are  derived  from  the  sense 
of  taste ;  sagacity,  from  the  dog's  extraordinary  power  of 
smell ;  but  as  the  sense  of  sight  is  by  far  the  most  acute 
and  intellectual,  it  gives  rise  to  the  larger  part  of  lan- 
guage ;  clearness,  lucidity,  obscurity,  haziness,  perspicuity, 
and  innumerable  other  expressions,  are  derived  from  this 
sense. 

It  is  truly  astonishing  to  notice  the  power  which  lan- 
guage possesses  by  the  processes  of  generalization,  speci- 
alization, and  metaphor,  to  create  many  words  from  one 
single  root.  Prof.  Max  Miiller  has  given  a  remarkable 
instance  of  this  in  the  case  of  the  root  spec,  which  means 
sight,  and  appears  in  the  Aryan  languages,  as  in  the  San- 
scrit spas,  the  Greek  o-KCTrro/iat,  with  transposition  of  con- 
sonants, in  the  Latin  specio,  and  even  in  the  English  spy. 
The  following  is  an  incomplete  list  of  the  words  deve- 
loped from  this  one  root ;  species,  special,  especial,  speci- 
men, spice,  spicy,  specious,  speciality,  specific,  specializa- 
tion, specie  (gold,  or  silver),  spectre,  specification,  spec 
tacle,  spectator,  spectral,  spectrum,  speculum,  specular, 
speculation.  The  same  root  also  enters  into  composi- 
tion with  various  prefixes;  and  we  thus  obtain  a  series 
of  words,  suspect,  aspect,  circumspect,  expect,  inspect, 


*i.l         THE  GROWTH  OF  LANGUAGE.          53 

prospect,  respect,  retrospect,  introspection,  conspicuous, 
perspicuity,  perspective;  with  each  6f  which,  again,  a 
number  of  derivatives  is  connected.  Thus,  from  suspect, 
we  derive  suspicion,  suspicable,  suspicious,  suspiciously, 
suspiciousness.  I  have  estimated  that  there  are  in  aU 
at  least  246  words,  employed  at  some  period  or  other  ir 
the  English  language  which  undoubtedly  come  from  the 
one  root  spec. 

J.  S.  Mill's  Logic,  Book  IV.  Chap.  i.  'On  the  Natural 
History  of  the  Variations  in  the  Meanings  of  Terms.' 
Archbishop  Trench,  On  the  Study  of  Words. 
Max  M  tiller,  Lectures  on  the  Science  of  Language. 


LESSON  VIL 
LEIBNITZ  ON   KNOWLEDGE. 

IN  treating  of  terms  it  is  necessary  that  we  should  clearly 
understand  what  a  perfect  notion  of  the  meaning  of  a 
term  requires.  When  a  name  such  as  monarch,  or  civili- 
zation, or  autonomy  is  used,  it  refers  the  mind  to  some 
thing  or  some  idea,  and  we  ought  if  possible  to  obtain 
a  perfect  knowledge  of  the  thing  or  idea  before  we  use 
the  word;  In  what  does  this  perfect  knowledge  consist  ? 
What  are  its  necessary  characters?  This  is  a  question 
which  the  celebrated  mathematician  and  philosopher 
Leibnitz  attempted  to  answer  in  a  small  treatise  or  tract 
first  published  in  the  year  1684.  This  tract  has  been  the 
^asis  of  what  is  given  on  the  subject  in  several  recent 
Vrks  on  Logic,  and  a  complete  translation  of  the  trad 


54  LEIBNITZ  ON  KNOWLEDGE.        \\ 

has  been  appended  by  Mr  Baynes  to  his  translation  oi 
the  Port  Royal  Logic.  As  the  remarks  of  Leibnitz  him- 
self  are  not  always  easy  to  understand,  I  will  not  confine 
myself  to  his  exact  words,  but  will  endeavour  to  give  the 
simplest  possible  statement  of  his  views,  according  as 
chey  have  been  interpreted  by  Dr  Thomson  or  Sir  W, 
Hamilton. 

Knowledge  is  either  obscure  or  clear ;  either  confused 
or  distinct;  either  adequate  or  inadequate;  and  lastly 
either  symbolical  or  intuitive.  Perfect  knowledge  must 
be  clear,  distinct,  adequate  and  intuitive ;  if  it  fails  in  any 
one  of  these  respects  it  is  more  or  less  imperfect.  We 
may,  therefore,  classify  knowledge  as  in  the  following 
scheme  — 

Knowledge. 
Clear.  Obscure. 


Distinct  Confused 

Adequate.  Inadequate. 

Intuitive.  Symbolical. 
Perfect. 

A  notion,  that  is  to  say  our  knowledge  of  a  thing,  is 

obsoure  when  it  does  not  enable  us  to  recognize  the  thing 
again  and  discriminate  it  from  all  other  things.  We 
have  a  clear  notion  of  a  rose  and  of  most  common  flowers 
because  we  can  recognise  them  with  certainty,  and  do  not 
confuse  them  with  each  other.  Also  we  have  a  clear 
notion  of  any  of  our  intimate  friends  or  persons  whom  we 
habitually  meet,  because  we  recognise  them  whenever  we 
see  them  with  the  utmost  certainty  and  without  hesita- 
tion. It  is  said  that  a  shepherd  acquires  by  practice  a 
clear  notion  of  each  sheep  of  his  nock,  so  as  to  enable 
him  to  single  out  any  one  separately,  and  a  keeper  of 


II.]          LEIBNITZ  OA  KNOWLEDGE.  55 

hounds  learns  the  name  and  character  of  each  hound, 
while  other  persons  have  only  an  obscure  idea  of  the 
nounds  generally,  and  could  not  discriminate  one  from 
the  other.  But  the  geologist  cannot  give  a  clear  idea  oi 
what  sandstone,  conglomerate,  or  schist,  or  slate,  or  trap 
rock  consists,  because  different  rocks  vary  infinitely  in 
degree  and  character,  and  it  is  often  barely  possible  tc 
say  whether  a  rock  is  sandstone  or  conglomerate,  schist 
or  slate,  and  so  on.  In  the  lower  forms  of  life  the  natu- 
ralist hardly  has  a  clear  notion  of  animal  life,  as  distin- 
guished from  vegetable  life ;  it  is  often  difficult  to  decide 
whether  a  protophyte  should  be  classed  with  animals  or 
plants. 

Clear  knowledge,  again,  is  confused,  when  we  cannot 
distinguish  the  parts  and  qualities  of  the  thing  known, 
and  can  only  recognise  it  as  a  whole.  Though  any  one 
instantly  knows  a  friend,  and  could  discriminate  him  from 
all  other  persons,  yet  he  would  generally  find  it  impos- 
sible to  say  how  he  knows  him,  or  by  what  marks.  He 
could  not  describe  his  figure  or  features,  but  in  the  very 
roughest  manner.  A  person  unpractised  in  drawing,  who 
attempts  to  delineate  even  such  a  familiar  object  as  a 
horse  or  cow,  soon  finds  that  he  has  but  a  confused  notion 
of  its  form,  while  an  artist  has  a  distinct  idea  of  the  form 
of  every  limb.  The  chemist  has  a  distinct  as  well  as  a 
clear  notion  of  gold  ai  d  silver,  for  he  can  not  only  tell 
with  certainty  whether  any  metal  is  really  gold  or  silver, 
but  he  can  specify  and  describe  exactly  the  qualities  by 
which  he  knows  it ;  and  could,  if  necessary,  mention  a 
great  many  other  qualities  as  well  We  have  a  very  dis- 
tinct notion  of  a  chess-board,  because  we  know  it  consists 
of  64  square  spaces;  and  all  our  ideas  of  geometrical 
figures,  such  as  triangles,  circles,  parallelograms  squares, 
pentagons,  hexagons,  &c.  are  or  ought  to  be  perfectly  dis- 
tinct. But  when  we  talk  of  a  constitutional  gov****nnt 


56  LEIBNITZ  ON  KNOWLEDGE        [LESS 

or  a  civilised  nation,  we  have  only  the  vaguest  idea  oi 
irnat  we  mean.  We  cannot  say  exactly  what  is  requisite 
to  make  a  Government  constitutional,  without  including 
aiso  Governments  which  we  do  not  intend  to  include; 
inJ  so  of  civilized  nations;  these  terms  have  neither  dis- 
tinct nor  clear  meanings. 

It  is  to  be  remarked  that  no  simple  idea,  such  as  that 
of  red  colour,  can  be  distinct  in  the  meaning  here  in- 
tended, because  nobody  can  analyse  red  colour,  or  de- 
scribe to  another  person  what  it  is.  A  person  who  haj 
been  blind  from  birth  cannot  be  made  to  conceive  it ;  and 
it  is  only  by  bringing  an  actual  red  object  before  the  eye 
that  we  can  define  its  character.  The  same  is  generally 
true  of  all  simple  sensations,  whether  tastes,  smells,  co- 
lours, or  sounds;  these  then  may  be  clearly  known,  but 
not  distinctly r,  in  the  meaning  which  Leibnitz  gives  to  this 
word. 

To  explain  the  difference  which  Leibnitz  intended  to 
denote  by  the  names  adequate  and  inadequate,  is  not 
easy.  He  says,  "When  everything  which  enters  into  a 
distinct  notion  is  distinctly  known,  or  when  the  last  ana- 
lysis is  reached,  the  knowledge  is  adequate,  of  which  I 
scarcely  know  whether  a  perfect  example  can  be  offered 
— the  knowledge  of  numbers,  however,  approaches  near 
to  it" 

To  have  adequate  knowledge  of  things,  then,  we  must 
not  only  distinguish  the  parts  which  make  up  our  notion 
of  a  thing,  but  the  parts  which  make  up  those  parts.  For 
mstance,  we  might  be  said  to  have  an  adequate  notion  of 
a  chess-board,  because  we  know  it  to  be  made  up  of  64 
squares,  and  we  know  each  of  those  squat  es  distinctly, 
because  each  is  made  up  of  4  equal  right  lines,  joined 
at  right  angles.  Nevertheless,  we  cannot  be  said  to  have 
a  distinct  notion  of  a  straight  line,  because  we  cannot  well 
define  it.  or  resolve  it  into  anything  simpler.  To  be  com. 


4.J          LEIBNITZ  ON  KNOWLEDGE.  §7 

pletely  adequate,  our  knowledge  ought  to  admit  of  analysis 
after  analysis  ad  infinitum,  so  that  adequate  knowledge 
would  be  impossible.  But,  as  Dr  Thomson  remarks,  we 
may  consider  any  knowledge  adequate  which  carries  thf 
analysis  sufficiently  far  for  the  purpose  in  view.  A  me- 
chanist,  for  instance,  has  adequate  knowledge  of  a  ma- 
chine, if  he  not  only  know  its  several  wheels  and  parts, 
out  the  purposes,  materials,  forms,  and  actions  of  those 
parts ;  provided  again  that  he  knows  all  the  mechanical 
properties  of  the  materials,  and  the  geometrical  properties 
of  the  forms  which  may  influence  the  working  of  the 
machine.  But  he  is  not  expected  to  go  on  still  further  and 
explain  why  iron  or  wood  of  a  particular  quality  is  strong 
or  brittle,  why  oil  acts  as  a  lubricator,  or  on  what  axioms 
the  principles  of  mechanical  forces  are  founded. 

Lastly,  we  must  notice  the  very  important  distinction 
of  symbolical  and  intuitive  knowledge.  From  the  original 
meaning  of  the  word,  intuitive  would  denote  that  which 
we  gain  by  seeing  (Latin,  intueor,  to  look  at),  and  any 
knowledge  which  we  have  directly  through  the  senses, 
or  by  immediate  communication  to  the  mind,  is  called 
intuitive.  Thus  we  may  learn  intuitively  what  a  square 
or  a  hexagon  is,  but  hardly  what  a  chiliagon,  or  figure  of 
i  coo  sides,  is. 

We  could  not  tell  the  difference  by  sight  of  a  figure 
of  1000  sides  and  a  figure  of  1001  sides.  Nor  can  we 
imagine  any  such  figure  completely  before  tht  mind.  It 
is  known  to  us  only  by  name  or  symbolically.  All  large 
numbers,  such  as  those  which  state  the  velocity  of  light 
(186,000  miles  per  second),  the  distance  of  the  sun 
(91,000,000  miles),  and  the  like,  are  known  tonis  only  by 
symbols,  and  they  are  beyond  our  powers  of  imagination. 

Infinity  is  known  in  a  similar  way,  so  that  we  can  in 
an  intellectual  manner  become  acquainted  with  that  o4 
which  our  senses  could  never  inform  us.  We  speak  alto 


5«  LEIBNITZ  ON  KNOWLEDGE.       [LES& 

of  nothing,  of  zero,  of  that  which  is  self-contradictory, 
of  the  non-existent,  or  even  of  the  unthinkable  or  incon- 
ceivable. although  the  words  denote  what  can  never  bf 
realized  in  the  mind  and  still  less  be  perceived  through 
the  senses  intuitively,  but  can  only  be  treated  in  a  merely 
symbolical  way. 

In  arithmetic  and  algebra  we  are  chiefly  occupied 
with  symbolical  knowledge  only,  since  it  is  not  necessary 
m  working  a  long  arithmetical  question  or  an  algebraical 
problem  that  we  should  realise  to  ourselves  at  each  step 
the  meaning  of  the  numbers  and  symbols.  We  learn 
from  algebra  that  if  we  multiply  together  the  sum  and 
difference  of  two  quantities  we  get  the  difference  of  the 
squares  ;  as,  in  symbols 


which  is  readily  seen  to  be  true,  as  follows  • 

a  +  b 
a-t 


-ab-P 


In  the  above  we  act  darkly  or  symbolically,  using  the 
letters  a  and  b  according  to  certain  fixed  rules,  without 
knowing  or  caring  what  they  mean ;  and  whatever  mean- 
ing we  afterwards  give  to  a  and  b  we  may  be  sure  the 
process  holds  good,  and  that  the  conclusion  is  true  with- 
out going  over  the  steps  again. 

But  in  geometry,  we  argue  by  intuitive  perception  oi 
the  truth  of  each  step,  because  we  actually  employ  a  re- 
presentation in  the  mind  of  the  figures  in  question,  and 
satisfy  ourselves  that  the  requisite  properties  are  really 
Dossessed  by  the  figures.  Thus  the  algebraical  truth 
•hown  above  in  symbols  may  be  easily  proved  to  hold  tru* 


HL]          LEIBNITZ  ON  KNOWLEDGE.  & 

of  lines  and  rectangles  contained  under  those  Hnes,  as  a 
corollary  of  the  5th  Prop,  of  Euclid's  Second  Book. 

Much  might  be  said  concerning  the  comparative  ad- 
vantages of  the  intuitive  and  symbolical  methods.  The 
Utter  is  usually  much  the  less  laborious,  and  gives  tht 
most  widely  applicable  answers ;  but  the  symbolical  sel- 
dom or  never  gives  the  same  command  and  comprehen- 
sion of  the  subject  as  the  intuitive  method.  Hence  the 
study  of  geometry  is  always  indispensable  in  education, 
although  the  same  truths  are  often  more  readily  proved 
by  algebra.  It  is  the  peculiar  glory  of  Newton  that  he 
was  able  to  explain  the  motions  of  the  heavenly  bodies 
by  the  geometric  or  intuitive  method ;  whereas  the  great- 
est of  his  successors,  such  as  Lagrange  or  Laplace,  have 
treated  these  motions  by  the  aid  of  symbols. 

What  is  true  of  mathematical  subjects  may  be  applied 
to  all  kinds  of  reasoning ;  for  words  are  symbols  as  much 
as  A,  B,  Ct  or  xt  y,  *,  and  it  is  possible  to  argue  with 
words  without  any  consciousness  of  their  meaning.  Thus 
if  I  say  that  "  selenium  is  a  dyad  element,  and  a  dyad 
element  is  one  capable  of  replacing  two  equivalents  of 
hydrogen,"  no  one  ignorant  of  chemistry  will  be  able  to 
attach  any  meaning  to  these  terms,  and  yet  any  one  will 
be  able  to  conclude  that  "  selenium  is  capable  of  replacing 
two  equivalents  of  hydrogen."  Such  a  person  argues  in  a 
purely  symbolical  manner.  Similarly,  whenever  in  com- 
mon life  we  use  words,  without  having  in  mind  at  the 
moment  the  full  and  precise  meaning  of  the  words,  we 
possess  symbolical  knowledge  only. 

There  is  no  worse  habit  for  a  student  or  reader  to 
acquire  than  that  of  accepting  words  instead  of  a  know- 
ledge of  things.  It  is  perhaps  worse  than  useless  to  read 
a  work  on  natural  history  about  Infusoria,  Foraminifera, 
Rotifera  and  the  like,  if  these  names  do  not  convey  cleai 
images  to  the  mind.  Nor  can  a  student  who  has  not 


60  LEIBNITZ  OX  KNOWLEDGE.       [LKSi 

mtnessed  experiments,  and  examined  the  substances  with 
his  own  eyes,  derive  any  considerable  advantage  from 
works  on  chemistry  and  natural  philosophy,  where  he  will 
meet  with  hundreds  of  new  terms  which  would  be  to  him 
mere  empty  and  confusing  signs.  On  this  account  we 
should  lose  no  opportunity  of  acquainting  ourselves,  by 
means  of  our  senses,  with  the  forms,  properties  and 
changes  of  things,  in  order  that  the  language  we  employ 
may,  as  far  as  possible,  be  employed  Intuitively,  and  we 
may  be  saved  from  the  absurdities  and  fallacies  into 
which  we  might  otherwise  fall.  We  should  observe,  in 
short,  the  advice  of  Bacon—  ipsis  consuescere  rtbus — 
to  accustom  ourselves  to  things  themselves. 

Hamilton's  Lectures  on  Logic.  Lect  IX 
Barnes'  Port  Royal  Logic.     Part  L  Chap.  9,  and  Ap- 
pendix. 


LESSON  VIIL 

KINDS  OF  PROPOSITIONS. 

A  TERM  standing  alone  is  not  capable  of  expressing  truth; 
it  merely  refers  the  mind  to  some  object  or  class  of  objects, 
about  which  something  may  be  affirmed  or  denied,  but 
about  which  the  term  itself  does  not  affirm  or  deny  any- 
thing. "Sun,"  "air,7*  "table,"  suggest  to  every  mind 
objects  of  thought,  but  we  cannot  say  that  "  sun  is  true," 
or  "  air  is  mistaken,"  or  "  table  is  false."  We  must  join 
words  or  terms  into  sentences  or  propositions  before  they 
can  express  those  reasoning  actions  of  the  mind  to  which 


viii.  1  KINDS  OF  PROPOSITIONS.  61 

truth  or  falsity  may  be  attributed.  "  The  sun  is  bright," 
"the  air  is  fresh,"  "the  table  is  unsteady,"  are  statements 
which  may  be  true  or  may  be  false,  but  we  can  certain!) 
entertain  the  question  of  their  triith  in  any  circumstances 
Now  as  the  logical  term  was  defined  to  be  any  comb  ma 
tion  of  words  expressing  an  act  of  simple  apprehension. 
so  a  logical  proposition  is  any  combination  of  words 
expressing  an  act  of  judgment.  The  proposition  is  in 
short  the  result  of  an  act  of  judgment  reduced  to  the  form 
of  language. 

What  the  logician  calls  a  proposition  the  grammarian 
calls  a  sentence.  But  though  every  proposition  is  a  sen- 
tence, it  is  not  to  be  supposed  that  every  sentence  is  a 
proposition.  There  are  in  fact  several  kinds  of  sentences 
more  or  less  distinct  from  a  proposition,  such  as  a  Sen- 
tence Interrogative  or  Question,  a  Sentence  Imperative 
or  a  Command,  a  Sentence  Optative,  which  expresses  a 
wish,  and  an  Exclamatory  Sentence,  which  expresses  an 
emotion  of  wonder  or  surprise.  These  kinds  of  sentence 
may  possibly  be  reduced,  by  a  more  or  less  indirect  mode 
of  expression,  to  the  form  of  a  Sentence  Indicative,  which 
is  the  grammatical  name  for  a  proposition ;  but  until  this 
be  done  they  have  no  proper  place  in  Logic,  or  at  least 
no  place  which  logicians  have  hitherto  sufficiently  ex- 
plained. 

The  name  proposition  is  derived  from  the  Latin  wordy 
pro,  before,  and  pono,  I  place,  and  means  the  laying  01 
placing  before  any  person  the  result  of  an  act  of  judg- 
ment. Now  every  act  of  judgment  or  comparison  must 
involve  the  two  things  brought  into  comparison,  and 
every  proposition  will  naturally  consist  of  three  parts—" 
the  two  terms  or  names  denoting  the  things  compared, 
and  the  copula  or  verb  indicating  the  connection  between 
them,  as  it  was  ascertained  in  the  act  of  judgment.  Thus 
the  proposition,  "  Gold  is  a  yellow  substance,"  expresses 


62  KINDS  OF  PROPOSITIONS.         [LESS, 

An  agreement  between  gold  and  certain  other  substances 
previously  called  yellow  in  regard  to  their  colour.  Gold 
and  yellow  substance  are  evidently  the  two  terms,  and  is 
the  copula. 

It  is  always  usual  to  call  the  first  term  of  a  proposl 
don  the  subject,  since  it  denotes  the  underlying  matter 
is  it  were  (Latin,  sub,  under,  and  jactum,  laid)  about 
which  something  is  asserted.  The  second  term  is  called 
the  predicate,  which  simply  means  that  which  is  affirmed 
or  asserted.  This  name  is  derived  from  the  Latin  prce- 
dicare,  to  assert,  whence  comes  the  French  name  predi- 
cateur,  corrupted  into  our  preacher.  This  Latin  verb  is 
not  to  be  confused  with  the  somewhat  similar  one  pre- 
dlcere,  which  has  the  entirely  different  meaning  to  pre- 
dict or  foretell.  I  much  suspect  that  newspaper  writers 
and  others,  who  pedantically  use  the  verb  "to  predi. 
cate,"  sometimes  fall  into  this  confusion,  and  really  mean 
to  predict,  but  it  is  in  any  case  desirable  that  a  purely 
technical  term  like  predicate  should  not  be  needlessly 
introduced  into  common  language,  when  there  are  so 
many  other  good  words  which  might  be  used.  This  and 
all  other  technical  scientific  terms  should  be  kept  to  their 
proper  scientific  use,  and  the  neglect  of  this  rule  injures 
at  once  the  language  of  common  life  and  the  language  of 
science. 

Propositions  are  distinguished  into  two  kinds,  accord- 
ing as  they  make  a  statement  conditionally  or  uncondi- 
•ionally.  Thus  the  proposition,  "If  metals  are  heated 
they  are  softened,"  is  conditional,  since  it  does  not  make 
an  assertion  concerning  metals  generally,  but  only  in  the 
circumstances  when  they  become  heated.  Any  circum- 
stance which  must  be  granted  or  supposed  before  the 
assertion  becomes  applicable  is  a  condition.  Conditional 
propositions  are  of  two  kinds,  Hypothetical  and  Disjunc- 
tive, but  their  consideration  will  be  best  deferred  to  a 


KINDS  OF  PROPOSITIONS.  6, 

subsequent  Lesson  (xix).  Unconditional  propositions 
are  those  with  which  we  shall  for  some  time  be  solely 
concerned,  and  these  are  usually  called  Categorical  Pro- 
positions, from  the  Greek  verb  Kanjyopf'w  (kategorM,  to 
assert  or  affirm). 

The  following  diagram  will  conveniently  represent  the 
classification  of  sentences  and  propositions  as  far  as  we 
have  yet  proceeded : — 

=  Proposition  \    *  ej°"c     J"  Hypothetical 
errogative      \  Condltlonal  \  Disjunctive. 


Sentence 


Imperative 
Optative 

.  Exclamatory 

It  is  now  necessary  to  consider  carefully  the  several 
kinds  of  categorical  propositions.  They  are  classified 
according  to  quality  and  according  to  quantity.  As  re- 
gards quality  they  are  either  affirmative  or  negative ;  as 
regards  quantity  they  are  either  universal  or  particular. 

An  affirmative  proposition  is  one  which  asserts  a  cer- 
tain agreement  between  the  subject  and  predicate,  so  that 
the  qualities  or  attributes  of  the  predicate  belong  to  the 
subject  The  proposition,  "  gold  is  a  yellow  substance," 
states  such  an  agreement  of  gold  with  other  yellow  sub- 
stances, that  we  know  it  to  have  the  colour  yellow,  as 
well  as  whatever  qualities  are  implied  in  the  name  sub- 
stance. A  negative  proposition,  on  the  other  hand,  as- 
serts a  difference  or  discrepancy,  so  that  some  at  least  of 
the  qualities  of  the  predicate  do  not  belong  to  the  sub- 
ject.  *  Gold  is  not  easily  fusible"  denies  that  the  qua- 
lity of  being  easily  fused  belongs  to  gold. 

Propositions  are  again  divided  according  to  quantity 
into  universal  and  particular  propositions.  If  the  propo- 
sition affirms  the  predicate  to  belong  to  the  whole  of  the 
wbject,  it  is  an  universal  proposition,  as  in  the  example 


OF  PROPOSITIONS.          [ 

•  all  metals  are  elements,"  which  affirms  that  the  quality 
of  being  undecomposable  or  of  being  simple  in  nature  it 
true  of  all  metals.  But  if  we  say  "  some  meta»s  are  brit- 
tle," the  quality  of  brittleness  is  affirmed  only  of  some 
indefinite  portion  of  the  metals,  and  there  is  nothing  in 
the  proposition  to  make  us  sure  that  any  certain  metal  is 
brittle.  The  name  particular  being  derived  from  the 
diminutive  of  the  Latin  pars  would  naturally  signify  a 
small  part,  but  in  logic  it  must  be  carefully  interpreted  as 
signifying  any  part,  from  the  smallest  fraction  up  to 
nearly  the  whole.  Particular  propositions  do  not  include 
cases  where  a  predicate  is  affirmed  of  the  whole  or  of 
none  of  the  subject,  but  they  include  any  between  these 
limits.  We  may  accordingly  count  among  particular 
propositions  all  such  as  the  following:— 

A  rery  few  metals  are  less  dense  than  water. 

Most  elements  are  metals. 

Many  of  the  planets  are  comparatively  small  bodies. 

Not  a  few  distinguished  men  have  had  distinguished 
sons. 

The  reader  must  carefully  notice  the  somewhat  subtle 
point  explained  further  on/:hat  the  particular  proposition 
though  asserting  the  predrcate  only  of  a  part  j>f  the  sub- 
ject, does  not  deny  it  to  be  true  of  the  whole.  I 

Aristotle,  indeed,  considered  that  there  were  alto- 
gether four  kinds  of  proposition  as  regards  quantity, 
namely  — 

f  Universal 


Proposition 

Singular 

I  Indefinite. 

The  singular  proposition  is  one  which  has  a 
Derm  for  its  subject,  as  m  — 

Socrates  was  very  wise 
London  is  a  vast  city. 


fill.]  KINDS  OF  PROPOSITIONS.  6l 

But  we  may  fairly  consider  that  a  singular  proposition 
is  an  universal  one  ;  for  it  clearly  refers  to  the  whole  ol 
the  subject,  which  in  this  case  is  a  single  individual  thing. 

Indefinite  or  indesignate  propositions  are  those  which 
we  devoid  of  any  mark  of  quantity  whatever,  so  that  the 
form  of  words  gives  us  no  mode  of  judging  whether  the 
predicate  is  applicable  to  the  whole  or  only  part  of  the 
subject.  Metals  are  useful,  Comets  are  subject  to  the  law 
of  gravitation,  are  indefinite  propositions.  In  reality, 
however,  such  propositions  have  no  distinct  place  in 
logic  at  all,  and  the  logician  cannot  properly  treat  them 
until  the  true  and  precise  meaning  is  made  apparent. 
The  predicate  must  be  true  either  of  the  whole  or  of  part 
of  the  subject,  so  that  the  proposition,  as  it  stands,  is 
clearly  incomplete  ;  but  if  we  attempt  to  remedy  this  and 
supply  the  marks  of  quantity,  we  overstep  the  proper 
boundaries  of  logic  and  assume  ourselves  to  be  acquainted 
with  the  subject  matter  or  science  of  which  the  proposi- 
tion treats.  We  may  safely  take  the  preceding  examples 
to  mean  "some  metals  are  useful"  and  "  all  comets  are 
subject  to  the  law  of  gravitation,"  but  not  on  logical 
grounds.  Hence  we  may  strike  out  of  logic  altogether 
the  class  of  indefinite  propositions,  on  the  understanding 
;hat  they  must  be  rendered  definite  before  we  treat  them. 
may  observe,  however,  that  in  the  following  lessons  I 
hallTrequeritly  use  propositions  in  the  indefinite  form  as 
examplesr~bn  the  understanding  that  where  no  sign  ol 
quantity  appears,  the  universal  quantity  is  to  be  assumed. 
It  is  probable  that  wherever  a  term  is  used  aj  one,  it  / 

_  ( 


ought  to  be  interpreted  as  meaning  the  whole  of  i 
But  however  this  may  be,  we  need  not  recognize  the  inde- 
finite  proposition  as  a  distinct  kind  ;  and  singular  propo- 
sitions having  been  resolved  into  universals,  there  remain 
•nly  the  two  kinds,  Universal  and  Particular. 

Remembering  now  that  there  are  two  kinds  of  prupv 


66  KINDS  OF  PROPOSITIONS.          [LESS 

•ition  as  regards  quality,  and  two  as  regards  quantity  wt 
•hall  be  able  to  form  altogether  four  varieties,  thus : — 

f  Universal  (^"native        A 
\Negative  B 

Proposition  < 

\  Negative  0 

The  vowel  letters  placed  at  the  right  hand  are  sym- 
bols or  abbreviated  names,  which  are  always  used  to 
denote  the  four  kinds  of  proposition;  and  there  will  be 
no  difficulty  in  remembering  their  meaning  if  we  observe 
that  A  and  I  occur  in  the  Latin  verb  affirmo,  I  affirm,  and 
E  and  0  in  nego,  I  deny. 

There  will  not  generally  be  any  difficulty  in  referring 
to  its  proper  class  any  proposition  that  we  meet  with  in 
writings.  The  mark  of  universality  usually  consists  of 
some  adjective  of  quantity,  such  as  all,  every,  each,  any, 
the  whole;  but  whenever  the  predicate  is  clearly  intended 
to  apply  to  the  whole  of  the  subject  we  may  treat  the  pro- 
position as  universal.  The  signs  of  a  particular  proposi- 
tion are  the  adjectives  of  quantity,  some,  certain,  a  few, 
many,  most,  or  such  others  as  clearly  indicate  part  ai 
Uast. 

The  negative  proposition  is  known  by  the  adverbial 
particle  not  being  joined  to  the  copula ;  but  in  the  propo- 
sition Bj  that  is  the  universal  negative,  we  frequently  use 
the  particle  no  or  none  prefixed  to  the  subject.  Thus, 
"  no  metals  are  compound,"  "  none  of  the  ancients  were 
acquainted  with  the  laws  of  motion,"  are  familiar  forms  oJ 
the  universal  negative. 

The  student  must  always  be  prepared  too  to  meet  with 
misleading  or  ambiguous  forms  of  expression.  Thus  the 
proposition,  "  all  the  metals  are  not  denser  than  water," 
might  be  taken  as  B  or  0,  according  as  we  interpret  it  tt 


Via.]          KINDS  OP  PROPOSITIONS.  6v 

mean  "no  metals  are  denser  than  water,"  or  "not  all 
the  metals,"  &c.,  the  last  of  course  being  the  true  sense 
The  little  adjective  few  is  very  subject  to  a  subtle  am- 
biguity of  this  kind ;  for  if  I  say  "few  books  are  at  one* 
learned  and  amusing,"  I  may  fairly  be  taken  to  assert 
that  a  few  books  certainly  are  so,  but  what  I  really  mean 
to  draw  attention  to  is  my  belief  that  "the  greater  num 
ber  of  books  are  not  at  once  learned  and  amusing."  A 
proposition  of  this  kind  is  generally  to  be  classed  rathei 
as  0  than  I.  The  word  some  is  subject  to  an  exactly 
similar  ambiguity  between  some  but  not  all,  and  some  at 
least,  it  may  be  all;  the  latter  appears  to  be  the  correct 
interpretation,  as  shewn  in  the  following  lesson  (p  79). 

As  propositions  are  met  with  in  ordinary  language 
they  are  subject  to  various  inversions  and  changes  of  the 
simple  logical  form. 

(1)  It  is  not  uncommon,  especially  in  poetry,  to  find 
the  predicate  placed  first,  for  the  sake  of  emphasis  01 
variety  ;  as  in  "  Blessed  are  the  merciful ;"  "  Comes  some- 
thing down  with  eventide  ;"  "  Great  is  Diana  of  the  Ephe- 
sians."    There  is  usually  no  difficulty  in  detecting  sucli 
an  inversion  of  the  terms,  and  the  sentence  must  then 
be  reduced  to  the  regular  order  before  being  treated  in 
logic. 

(2)  The  subject  may  sometimes  be  mistaken  for  the 
predicate  when  it  is  described  by  a  relative  clause,  stand- 
ing at  the  end  of  the  sentence,  as  in  "  no  one  is  free  who 
is  enslaved  by  his  appetites."     Here  free  is  evidently 
the  predicate,  although  it  stands  in  the  middle  of  the 
sentence,  and  "one  who  is  enslaved  by  his  appetites* 
is  the  real  subject     This  proposition  is  evidently  of  the 
form  R. 

Propositions  are  also  expressed  in  various  modes  dif- 
fering from  the  simple  logical  order,  and  some  of  UM 
different  kinds  which  arise  must  be  noticed. 


68  KINDS  OF  PROPOSITIONS.          [l 

Exclusive  propositions  contain  some  words,  such  at 
only,  alone,  none  but,  which  limit  the  predicate  to  the 
subject  Thus,  in  "elements  alone  are  metals,"  we  arc 
informed  that  the  predicate  "metal"  cannot  be  applied  to 
anything  except  "elements,"  but  we  are  not  to  understand 
that  "all  elements  are  metals."  The  same  meaning  is 
expressed  by  "  none  but  elements  are  metals  f  or,  again, 
by  "  all  that  are  not  elements  are  not  metals  f  and  this  we 
shall  see  in  the  next  lesson  is  really  equivalent  to  "all 
metals  are  elements."  Arguments  which  appear  fallacious 
at  first  sight  will  often  be  found  correct  when  they  con- 
tain exclusive  propositions  and  these  are  properly  inter- 
preted. 

Exceptive  propositions  affirm  a  predicate  of  all  the 
subject  with  the  exception  of  certain  defined  cases,  to 
which,  as  is  implied,  the  predicate  does  not  belong.  Thus, 
"  all  the  planets,  except  Venus  and  Mercury,  are  beyond 
the  earth's  orbit,"  is  a  proposition  evidently  equivalent  to 
two,  viz.  that  Venus  and  Mercury  are  not  beyond  the 
earth's  orbit,  but  that  the  rest  are.  If  the  exceptions 
are  not  actually  specified  by  name  an  exceptive  proposi- 
tion must  often  be  treated  as  a  particular  one.  For  il 
1  say  "  all  the  planets  in  our  system  except  one  agree  with 
Bode's  law,"  and  do  not  give  the  name  of  that  one  excep- 
tion, the  reader  cannot,  on  the  ground  of  the  proposition, 
assert  of  any  planet  positively  that  it  does  agree  with 
Bode's  law. 

Some  propositions  are  distinguished  as  explicative  01 
essential,  because  they  merely  affirm  of  their  subject  a 
predicate  which  is  known  to  belong  to  it  by  all  who  can 
define  the  subject.  Such  propositions  merely  unfold 
what  is  already  contained  in  the  subject.  "A  parallelo- 
gram has  four  sides  and  four  angles,"  is  an  explicative  or 
essential  proposition.  "  London,  which  is  the  capital  oi 
England,  is  the  largest  city  of  Europe/'  contains  two  pro- 


VIIL]  KINDS  OF  PROPOSITIONS.  69 

positions ;  of  which  one  merely  directs  our  attention  to 
a  fact  which  all  may  be  supposed  to  know,  viz,  that 
London  is  the  capital  of  England. 

Ampllative  propositions,  on  the  other  hand,  join  a 
new  predicate  to  the  subject  Thus  to  those  who  do  not 
know  the  comparative  sizes  of  cities  in  Europe,  the  last 
example  contains  an  ampliative  proposition.  The  greater 
number  of  propositions  are  of  this  kind. 

Tautologoua  or  Truistlo  propositions  are  those  which 
merely  affirm  the  subject  of  itself,  and  give  no  informa- 
tion whatever;  as  in,  "whatever  is,  is;"  "what  I  have 
written,  I  have  written." 

It  is  no  part  of  formal  Logic  to  teach  us  how  to  inter- 
pret the  meanings  of  sentences  as  we  meet  them  in  writ- 
ings ;  this  is  rather  the  work  of  the  grammarian  and 
philologist  Logic  treats  of  the  relations  of  the  different 
propositions,  and  the  inferences  which  can  be  drawn  from 
them;  but  it  is  nevertheless  desirable  that  the  reader 
should  acquire  some  familiarity  with  the  real  logical 
meaning  of  conventional  or  peculiar  forms  of  expression, 
and  a  number  of  examples  will  be  found  at  the  end  of 
the  book,  which  the  reader  is  requested  to  classify  and 
treat  as  directed. 

In  addition  to  the  distinctions  already  noticed  it  has 
long  been  usual  to  distinguish  propositions  as  they  are 
pore  or  modal.  The  pure  proposition  simply  asserts  that 
the  predicate  does  or  does  not  belong  to  the  subject,  while 
the  modal  proposition  states  this  cum  modo,  or  with  an 
intimation  of  the  mode  or  manner  in  which  the  predicate 
belongs  to  the  subject  The  presence  of  any  adverb  of 
time,  place,  manner,  degree,  &c^  or  any  expression  equi- 
valent to  an  adverb,  confers  modality  on  a  proposition. 
"Error  is  always  in  haste;"  "justice  is  ever  equal;"  "a 
perfect  man  ought  always  to  be  conquering  himself,"  are 

nples  of  modal  propositions  in  this  acceptation  ol 


70  KINDS  OF  PROPOSITIONS.         [LEsa 

the  name.  Other  logicians,  however,  have  adopted  a 
different  view,  and  treat  modality  as  consisting  in  the 
decree  of  certainty  or  probability  with  which  a  judgment 
is  made  and  asserted.  Thus,  we  may  say,  "  an  equilateral 
triangle  is  necessarily  equiangular ;"  "  men  are  generally 
trustworthy  f  "  a  falling  barometer  probably  indicates  a 
coming  storm ;"  "Aristotle's  lost  treatises  may  possibly  be 
recovered  ?  and  all  these  assertions  are  made  with  a  dif- 
ferent degree  of  certainty  or  modality.  Dr  Thomson  is 
no  doubt  right  in  holding  that  the  modality  does  not 
affect  the  copula  of  the  proposition,  and  the  subject  could 
only  be  properly  treated  in  a  work  on  Probable  Reason- 
ing. 

Many  logicians  have  also  divided  proposition*  ac- 
cording as  they  are  true  or  false,  and  it  might  well  seem 
to  be  a  distinction  of  importance.  Nevertheless,  it  is 
wholly  beyond  the  province  of  the  logician  to  consider 
whether  a  proposition  is  true  or  not  in  itself;  all  that  he 
has  to  determine  is  the  comparative  truth  of  propositions 
— that  is,  whether  one  proposition  is  true  when  another 
is.  Strictly  speaking,  logic  has  nothing  to  do  with  a  pro- 
position by  itself;  it  is  only  in  converting  or  transmuting 
certain  propositions  into  certain  others  that  the  work  of 
reasoning  consists,  and  the  truth  of  the  conclusion  is  only 
so  far  in  question  as  it  follows  from  the  truth  of  what  we 
shall  call  the  premises.  It  is  the  duty  of  the  special  sci- 
ences each  in  its  own  sphere  to  determine  what  are  true 
propositions  and  what  are  false,  and  logic  would  be  but 
mother  name  for  the  whole  of  knowledge  could  it  take 
this  duty  on  itself. 

See  Mr  Mill's  System  of  Logic ;  Book  I.  Chap.  IT, 
which  generally  agrees  with  what  is  given  above.  Chap- 
ters V.  and  vi.  contain  Mr  Mill's  views  on  the  Nature 
tad  Import  of  Propositions,  which  subject  may  be  furthei 


IX  ]  THE  OPPOSITION  OF  PROPOSITIONS.  7, 

studied  in  Mr  Mill's  Examination  of  Sir  W.  Hamilton'* 
Philosophy,  Chap.  xvin. ;  Hamilton's  Lectures  on  Lcgic^ 
No.  xiii.;  and  MansePs  Prolegomena  Logica,  Chap.  II.; 
but  the  subject  is  too  metaphysical  in  character  to  be 
treated  in  this  work. 


LESSON   IX. 
THE  OPPOSITION   OF  PROPOSITIONS. 

WE  have  ascertained  that  four  distinct  kinds  of  propo- 
sitions are  recognized  by  logicians, — the  Universal  affirm- 
ative, the  Particular  affirmative,  the  Universal  negative, 
and  the  Particular  negative,  commonly  indicated  by  the 
symbols  A,  I,  E,  0.  It  is  now  desirable  to  compare  toge- 
ther somewhat  minutely  the  meaning  and  use  of  proposi- 
tions of  these  various  kinds,  so  that  we  may  clearly  learn 
how  the  truth  of  one  will  affect  the  truth  of  others,  or  how 
the  same  truth  may  be  thrown  into  various  forms  of  ex- 
pression. 

The  proposition  A  expresses  the  fact  that  the  thing  or 
el-ass  of  things  denoted  by  the  subject  is  included  in,  and 
forms  part  of  the  class  of  things  denoted  by  the  predicate. 
Thus  "  all  metals  are  elements"  means  that  metals  form 
a  part  of  the  class  of  elements,  but  not  the  whole.  Ai 
there  are  altogether  63  known  elements,  of  which  48  are 
metals,  we  cannot  say  that  all  elements  are  metals.  The 
proposition  itself  does  not  tell  us  anything  about  element* 
in  general;  it  is  not  in  fact  concerned  with  elements, 
metals  being  the  subject  about  which  it  gives  us  informa 


fa  THE  OPPOSITION  |LKSi 

don.  This  is  best  indicated  by  a  kind  of  diagram,  first 
osed  by  the  celebrated  mathematician  Euler,  in  his  lettert 
to  a  German  princess.  In  Fig.  I,  the  metals  are  supposed 
to  be  enclosed  in  the  small  circle  somewhat  as  sheep 
Slight  be  in  a  pinfold,  this  circle  containing  all  the  metals 
ind  nothing  else.  The  greater  circle  is  supposed  to  con- 
tain in  a  similar  manner  all  the  elements  and  nothing 
else  Now  as  the  small  circle  is  wholly  within  the  larger 
one,  it  follows  that  all  the  metals  must  be  counted  aa 

Fig... 


dements,  but  of  the  part  of  the  elements  outside  the 
circle  of  metals  we  know  nothing  from  the  proposition. 

The  particular  affirmative  proposition  I  exactly  resem- 
bles A  in  meaning,  except  that  only  part  of  the  subject  is 
brought  into  question.  When  I  say  that  "  some  metals 
are  brittle,"  I  mean  that  of  a  collection  of  all  the  dif- 
ferent metals  a  few  at  least  might  be  picked  out  which 
would  be  found  to  be  brittle  ;  but  the  word  some  is  ex- 
ceedingly indefinite,  shewing  neither  the  exact  number  ol 
brittle  metals,  nor  how  we  are  to  know  them  from  the 
others,  unless  indeed  by  trying  whether  they  are  brittle. 
This  proposition  will  be  properly  represented  in  Eider's 
mode  by  two  intersecting  circles,  one  supposed  to  enclose 
all  metals,  and  the  other  all  brittle  substances.  Th« 
mere  fact  of  the  two  circles  intersecting  proves  that  som* 


OL] 


OF  PROPOSITIONS. 
Fig... 


part  of  one  class  must  coincide  with  some  part  of  the 
other  class,  which  is  what  the  proposition  is  intended  to 
express.  Concerning  the  portions  of  the  circles  which  dc 
not  overlap  the  proposition  tells  us  nothing. 

The  universal  negative  proposition  E  denies  the  ex- 
istence  of  any  agreement  or  coincidence  between  the  sub- 
ject and  predicate.  Thus  from  "  no  metals  are  compound 
substances,"  we  learn  that  no  metal  is  to  be  found  among 
compound  substances,  and  it  follows  necessarily  that  no 
compound  substance  can  be  found  among  the  metals. 
For  were  there  a  compound  substance  among  the  metals, 
there  would  evidently  be  one  metal  at  least  among  the 
compound  substances.  This  entire  separation  in  thought 
of  the  two  classes  is  well  shewn  in  Killer's  method  by 
two  disconnected  circles. 

Fig.  3- 
|          JMofe         ]  [     Comfowidt.     | 

The  leader  will  easily  see  that  the  proposition  8  » 


f4  THE  OPPOSITION 

distinguished  from  A  and  I,  by  the  fact  that  it  gives  us 
some  information  concerning  the  whole  of  the  predicate^ 
because  we  learn  that  none  of  the  objects  included  in  the 
predicate  can  be  found  among  those  included  in  the  sub 
lect  The  affirmative  propositions,  on  the  other  hand, 
warranted  as  in  holding  that  the  objects  denoted  by  thi 
subject,  or  some  particular  part  of  them,  were  included  in 
the  predicate,  but  they  give  us  no  warrant  for  saying 
that  any  specified  part  of  the  predicate  is  in  the  subject 
Because  we  merely  know  that  a  substance  is  an  element, 
we  do  not  learn  from  the  proposition  "  all  metals  are  ele- 
ments" whether  it  is  a  metal  or  not.  And  from  the  pro- 
position "  some  metals  are  brittle,"  we  certainly  cannot 
ascertain  whether  any  particular  brittle  substance  is  a 
•netal.  We  must  seek  the  information  from  other  sources. 
But  from  "no  metals  are  compounds"  we  learn  of  any 
compour  1  substance  that  it  is  not  a  metal,  as  well  as  of 
a  metal  *hat  it  is  not  a  compound  substance. 

The  important  difference  above  explained  is  expressed 
in  technical  language  by  saying  that  the  proposition  E 
distributes  its  predicate,  whereas  the  affirmative  proposi- 
tions A  and  I  do  not  distribute  their  predicates.  By  dis- 
tribution of  a  term  is  simply  meant  taking  it  universally^ 
or  referring  to  all  parts  of  it;  and  as  the  validity  of  any 
argument  or  syllogism  will  usually  depend  upon  the  suffi- 
cient distribution  of  the  terms  occurring  in  it,  too  much 
mention  cannot  be  paid  to  this  point 

Judging  from  the  examples  we  have  had,  it  will  be 
seen  that  the  universal  affirmative  distributes  its  subject, 
bat  not  its  predicate  ;  for  it  gives  us  some  information 
concerning  all  metals,  but  not  all  elements.  The  parti- 
cular affirmative  distributes  neither  subject  nor  predicate; 
for  we  do  not  learn  anything  from  our  example  concern- 
'ng  all  metals  nor  concerning  all  brittle  substances.  ^ut 
niversal  negative  distributes  both  subject  and  predi- 


OF  PROPOSITIONS. 


7$ 


cate,  for  we  learn  something  of  all  metals  and  also  of  *A 
compound  substances. 

The  particular  negative  proposition  0  will  be  found  to 
distribute  its  predicate,  but  not  its  subject.  When  I  say 
some  metals  are  not  brittle,  I  intentionally  refer  only  to 
a  part  of  the  metals,  and  exclude  them  from  the  class 
of  brittle  substances  ;  but  I  cannot  help  at  the  same  time 
referring  to  the  whole  of  the  brittle  substances.  If  the 
metals  in  question  coincided  with  any  part  of  the  brittle 
substances  they  could  not  be  said  to  be  excluded  from 
the  class.  To  exclude  a  thing  from  any  space,  as  from 
a  particular  chamber  of  a  house,  it  must  not  merely  be 
removed  from  some  part,  but  from  any  part,  or  from  the 
whole  of  that  space  or  chamber.  Ruler's  diagram  for 
this  proposition  may  be  constructed  in  the  same  manner 
as  for  the  proposition  I  as  follows : — 
Fig.  4. 


It  is  apparent  that  though  part  of  the  metals  fall  into 
the  circle  of  brittle  substances,  yet  the  remaining  portion 
are  excluded  from  any  part  of  the  predicate. 

We  may  state  the  result  at  which  we  have  now  arrived 
in  the  following  form  :— 


(Universal  \  Affirmative  A. 
(  Negative      E. 
Particular  i  Affirmative  *• 
j  Negative      0. 

Subject. 
Distributed 
Distributed 
Undistributed. 
Undistributed 

Predicate. 
Undistributed 
Distributed 
Undistributed 
Distributed 

76  THE  OPPOSITION  [LESS 

We  shall  now  discover  with  great  ease  the  relations  oi 
the  four  propositions,  each  to  each,  that  is  to  say,  the  way 
m  which  they  are  opposed  to  each  other.  It  is  obvious 
that  the  truth  of  one  proposition  interferes  more  or  less 
completely  with  the  truth  of  another  proposition  having 
the  same  subject  and  predicate.  If  "  all  metals  are  ele- 
ments," it  is  impossible  that  "some  metals  are  not  ele- 
ments," and  still  more  palpably  impossible,  so  to  say,  that 
'•*  no  metals  should  be  elements."  The  proposition  A,  then, 
is  inconsistent  with  both  E  and  0 ;  and,  vice  versd,  E  and 
0  are  inconsistent  with  A.  Similarly,  B  is  inconsistent 
with  A  and  X.  But  this  important  difference  must  be  noted, 
that  if  A  be  false,  0  is  necessarily  true,  but  E  may  or  may 
not  be  true.  If  it  is  not  true  that  "  all  men  are  sincere," 
it  follows  that  "  some  men  are  not  sincere,"  but  it  does 
not  in  the  least  follow  that  "  no  men  are  sincere,"  This 
difference  is  expressed  by  saying  that  A  and  0  are  con- 
tradictory propositions,  whereas  A  and  B  are  called  oon- 
fcrmzy  propositions.  It  is  plain  that  A  and  B,  as  in  "  all 
men  are  sincere"  and  "no  men  are  sincere,"  represent 
the  utmost  possible  contrariety  of  circumstances.  ID 
order  to  prove  the  falsity  of  A,  it  is  sufficient  to  establish 
the  truth  of  0,  and  it  is  superfluous,  even  if  possible,  to 
prove  E  ;  similarly  B  is  disproved  by  proving  I,  and  il 
is  superfluous  to  prove  A.  Any  person  who  asserts  a  uni- 
versal proposition,  either  A  or  B,  lays  himself  under  the 
necessity  of  explaining  away  or  disproving  every  single 
exception  brought  agaii  t  it  An  opponent  may  always 
restrict  himself  to  the  uch  easier  task  of  finding  in- 
stances which  apparent  or  truly  contradict  the  univer- 
sality of  the  statement,  •  \t  if  he  takes  upon  himself  tc 
•firm  the  direct  contrary,  be  is  himself  open  to  easy  at- 
tack. Were  it  to  be  asserted,  for  instance,  that  "All 
Christians  are  more  moral  than  Pagans,"  it  would  be 
«asy  to  adduce  examples  showing  that  "  Some  Christians 


nt]  of  PROPOSITIONS.  n 

are  not  more  moral  than  Pagans,"  but  it  would  be  absurd 
to  suppose  that  it  would  be  necessary  to  go  to  the  con- 
trary extreme,  and  shew  that  "  No  Christians  are  mow 
moral  than  Pagans."  In  short  A  is  sufficiently  and  best 
disproved  by  0,  and  E  by  I.  It  will  be  easily  apparent 
that,  vict  versa,  0  is  disproved  by  A,  and  I  by  E ;  nor  is 
there,  indeed,  any  other  mode  at  all  of  disproving  these 
particular  propositions. 

When  we  compare  together  the  propositions  I  and  0 
we  find  that  they  are  in  a  certain  sense  contrary  in  na- 
ture, one  being  affirmative  and  the  other  negative,  but 
that  they  are  still  consistent  with  each  other.  It  is  true 
both  that  "  Some  metals  are  brittle,"  for  instance  Anti- 
mony, Bismuth  and  Arsenic ;  but  it  is  also  true  that 
"  Some  metals  are  not  brittle."  And  the  reader  will  ob- 
serve that  when  I  affirm  "  Some  metals  are  elements," 
there  is  nothing  in  this  to  prevent  the  truth  of  "  Some 
metals  are  not  elements,"  although  on  other  grounds  we 
know  that  this  is  not  true.  The  propositions  I  and  0  are 
called  subcontraries  each  of  the  other,  the  name  con- 
noting a  less  degree  of  contrariety  than  exists  between  A 
and  E. 

As  regards  the  relation  of  A  to  I  and  B  to  0,  it  is  plain 
that  the  truth  of  the  universal  includes  and  necessitates 
the  truth  of  the  particular  What  may  be  affirmed  or 
denied  of  all  parts  of  a  class  may  certainly  be  affirmed  or 
denied  similarly  of  some  part  of  the  class.  From  the 
truth  of  the  particular  we  have  no  right  to  infer  either 
the  truth  or  falsity  of  the  universal  of  the  same  quality. 
These  pairs  of  propositions  are  called  subalterns,  i.e. 
one  under  the  other  (Latin  sub  under,  and  alter  the  other 
af  two),  or  we  may  say  more  exactly  that  I  and  0  are 
respectively  the  subaltcrnates  of  A  and  B,  each  of  which 
is  a  subalternans. 


THE  OPPOSITION  [Li 

Thlp  relations  of  the  propositions  just  described 
•11  clearly  shown  in  the  following  scheme  : — 


Contraries   ...............  B 


rv 


I  ............  Subcontraries 


It  is  so  highly  important  to  apprehend  completely  and 
readily  the  consistency  or  opposition  of  propositions,  that 
I  will  put  the  matter  in  another  form.  Taking  any  two 
propositions  having  the  same  subject  and  predicate,  they 
must  come  under  one  of  the  following  statements  :  — 

1.  Of  contradictory  propositions,   one  must  be  true 
and  one  false. 

2.  Of  contrary  propositions,  both  cannot  be  true,  and 
both  may  be  false. 

3.  Of  subcontrary  propositions,  one  only  can  be  false, 
and  both  may  be  true. 

4.  Of  subalterns,  the  particular  is  true  if  the  universal 
be  true  ;  but  the  universal  may  or  may  not  be  true  when 
the  particular  is  true. 

I  put  the  same  matter  in  yet  another  form  in  the  fol- 
lowing table,  which  shows  how  the  truth  of  each  of  A,  £ 
I,  and  0,  affects  the  truth  of  each  of  the  ethers. 


DL]  OF  PROPOSITIONS.  « 

A  E  I               0 

is  is  is            is 

If  A  be  true          true  false  true         false, 

„  B   „      „           false  true  false         true. 

„  I    „     „        doubtful  false  true      doubtful 

„  0   „     „           false  doubtful  doubtful     true. 

It  will  be  evident  that  from  the  affirmation  of  univer 
sals  more  information  is  derived  than  from  the  affirmation 
of  particulars.  It  follows  that  more  information  can  b« 
derived  from  the  denial  of  particulars  than  from  the 
denial  of  universals,  that  is  to  say,  there  are  less  cases  left 
doubtful,  as  in  the  above  table. 

The  reader  may  well  be  cautioned,  however,  against 
an  ambiguity  which  has  misled  some  even  of  the  most 
eminent  logicians.  In  particular  propositions  the  adjec 
tive  some  is  to  be  carefully  interpreted  as  some,  and  there 
may  or  may  not  be  more  or  all.  Were  we  to  interpret  it 
as  some,  not  more  nor  all,  then  it  would  really  give  to  the 
proposition  the  force  of  I  and  0  combined.  If  I  say  "  some 
men  are  sincere,"  I  must  not  be  taken  as  implying  that 
"  some  men  are  not  sincere ;"  I  must  be  understood  to 
predicate  sincerity  of  some  men,  leaving  the  character  of 
the  remainder  wholly  unaffected.  It  follows  from  this 
that,  when  I  deny  the  truth  of  a  particular,  I  must  not  be 
understood  as  implying  the  truth  of  the  universal  of  the 
same  quality.  To  deny  the  truth  of  "  some  men  are  mor- 
tal" might  seem  very  natural,  on  the  ground  that  not  some 
but  All  men  are  mortal ;  but  then  the  proposition  denied 
would  really  be  some  men  are  not  mortal,  i.  e.  0  not  I. 
Hence  when  I  deny  that  "  some  men  are  immortal"  I 
mean  that  "no  men  are  immortal ;"  and  when  I  deny  that 
"some  men  are  not  mortal,"  I  mean  that  "all  men  are 
mortal." 

It  has  long   been  usual  to  compare  propositions  af 


So    OPPOSITION  OF  PROPOSITIONS.  [LESS.  IX 

regards  the  quality  of  the  subject  matter  to  which  the) 
refer,  and  what  is  technically  called  the  matter  was  dis- 
tinguished into  three  kinds,  necessary,  contingent,  and  im 
possible.  Necessary  matter  consists  of  any  subject  it 
which  the  proposition  A  may  be  affirmed ;  impossible  ii 
which  B  may  be  affirmed.  Any  subject  or  branch  of  know- 
ledge  in  which  universal  statements  cannot  usually  be 
made  is  called  contingent  matter,  and  it  implies  the  truth 
of  I  and  O.  Thus  "comets  are  subject  to  gravitation," 
though  an  indefinite  or  indesignate  proposition  vp.  65), 
may  be  interpreted  as  A,  because  it  refers  to  a  part  of 
natural  science  where  such  general  laws  obtain.  But 
"men  are  sincere"  would  be  properly  interpreted  as  par- 
ticular or  X,  because  the  matter  is  clearly  contingent.  The 
truth  of  the  following  statements  is  evident. 

In  necessary  matter  A  and  I  are  true ;  E  and  0  false. 

In  contingent  matter  I  and  O  are  true ;  A  and  E  false. 

Inimpossible  matter  E  and  0  are  true  ;  A  and  I  false. 

In  reality,  however,  this  part  of  logical  doctrine  is 
thoroughly  illogical,  because  in  treating  a  proposition  we 
have  no  right,  as  already  explained  (p.  70),  to  assume 
ourselves  acquainted  with  the  science  to  which  it  refers. 
Our  duty  is  to  elicit  the  exact  consequences  of  any  state- 
ments given  to  us.  We  must  learn  in  logic  to  transform 
information  in  every  possible  way,  but  not  to  add  extra- 
o«ms  facts. 


LESSON   X, 

CONVERSION   OF  PROPOSITIONS,  AND 
IMMEDIATE   INFERENCE. 

WE  are  said  to  infer  whenever  we  draw  one  truth 
from  another  truth,  or  pass  from  one  proposition  to 
another.  As  Sir  W.  Hamilton  says,  Inference  is  "the 
carrying  out  into  the  last  proposition  what  was  virtually 
contained  in  the  antecedent  judgments."  The  true 
sphere  of  the  science  oj"  logic  indeed  is  to  teach  the 
principles  on  which  this  act  of  inference  must  be  per- 
formed, and  all  the  ^previous  consideration  of  terms 
and  propositions  is  only  useful  or  pertinent  so  far  as 
it  assists  us  to  understand  the  processes  of  inference. 
We  have  to  consider  in  succession  all  the  modes  in 
which  the  same  information  may  be  moulded  into  differ- 
ent forms  of  expression  often  implying  results  of  an 
apparently  different  character.  Logicians  are  not  agreed 
exactly  as  to  what  we  may  include  under  the  name 
Inference,  and  what  we  should  not.  All  would  allow 
that  there  is  an  act  of  inference  when  we  see  drops  oi 
abater  on  the  ground  and  believe  that  it  has  rained. 
This  is  a  somewhat  complicated  act  of  inference,  which 
are  shall  consider  in  later  lessons  under  the  subject  ol 
Induction.  Few  or  none  would  say  that  there  is  an  act 
of  inference  in  passing  from  "  The  Duke  of  Cambridge 
is  the  Commander-in-chief,"  to  "The  Commander-in- 
chief  is  the  Duke  of  Cambridge."  But  without  paying 
much  regard  to  the  name  of  the  process  I  shall  in  this 


la        CONVERSION  OF  PROPOSITIONS,     [LKS8 

lesson  point  out  all  the  ways  in  which  we  can  from  a 
•ingle  proposition  of  the  forms  A,  E,  I  or  0,  pass  to  anothei 
proposition. 

We  are  said  to  convert  a  proposition  when  we 
transpose  its  subject  and  predicate ;  but  in  order  thai 
the  converse  or  converted  proposition  shall  be  inferred 
from  the  convertend,  or  tkat  which  was  to  be  converted, 
we  must  observe  two  rules  (i)  the  quality  of  the^pro- 
position  f  affirmative  or  negative^  must  be  preserved^  and 
(2)  no  term  must  be  .distributed  in  the  Converse  unless  it 
was  atstr^igdin  the  Convertend. 

If  in  "all  metals  are  elements"  we  were  simply  to 
transpose  the  terms,  thus — "  all  elements  are  metals,"  we 
imply  a  certain  knowledge  about  all  elements,  whereas 
it  has  been  clearly  shewn  that  the  predicate  of  A  is  un- 
distributed, and  that  the  convertend  does  not  really  give 
us  any  information  concerning  all  elements.  All  that 
we  can  infer  is  that  "some  elements  are  metals;"  this 
converse  proposition  agrees  with  the  rule,  and  the  pro- 
cess by  which  we  thus  pass  from  A  to  I  is  called  Con- 
vorsion  by  Lim^^on,  or  Per  accidens. 

When  the  converse  is  a  proposition  of  exactly  the 
same  form  as  the  convertend  the  process  is  called  simple 
MinvraHmi  Thus  from  "some  metals  are  brittle  sub- 


stances" I  can  infer  "some  brittle  substances  are 
metals,"  as  all  the  terms  are  here  undistributed.  Thus 
I  is  simply  converted  into  I. 

Again,  from  "  no  metals  are  compounds,"  I  can  pass 
directly  to  "no  compounds  are  metals,"  because  these 
propositions  are  both  in  B,  and  all  the  terms  are  there- 
fore distributed.  Euler's  diagram  (p.  73,  Fig.  3)  clearly 
shows,  that  if  all  the  metals  are  separated  from  all  the 
compounds,  all  the  compounds  are  necessarily  separate* 
from  all  the  metals.  The  proposition  £  is  then  simply 
converted  into  & 


*.]         AND  IMMEDIATE  INFERENCE.  S| 

But  in  attempting  to  convert  the  proposition  0  w« 
encounter  a  peculiar  difficulty,  because  its  subject  is  un- 
distributed; and  yet  the  subject  should  become  by  con- 
version the  predicate  of  a  negative  proposition,  which 
distributes  its  predicate.  Take  for  example  the  propo- 
sition, "some  existing  things  are  not  material  substances." 
By  direct  conversion  this  would  become  "all  material 
substances  are  not  existing  things  f  which  is  evidently 
absurd.  The  fallacy  arises  from  existing  things  being 
distributed  in  the  converse,  whereas  it  is  particular  in 
the  convertend ;  and  the  rules  of  the  Aristotelian  logic 
prevent  us  from  inserting  the  sign  of  particular  quantity 
before  the  predicate.  The  converse  would  be  equally 
untrue  and  fallacious  were  we  to  make  the  subject  par- 
ticular, as  in  "  some  material  substances  are  not  exist- 
ing things."  We  must  conclude,  then,  that  the  propo- 
sition 0  cannot  be  treated  either  by  simple  conversion  or 
conversion  by  limitation.  It  is  requisite  to  apply  a  new 
process,  which  may  be  called  Conversion  by  Negation, 
and  which  consists  in  first  changing  ^Ke  convertend  into 
an  affirmative  proposition,  and  then  converting  it  simply. 
If  we  attach  the  negation  to  the  predicate  instead  of 
to  the  copula,  the  proposition  becomes  "some  exist- 
ing things  are  immaterial  substances,"  and,  converting 
simply,  we  have — "some  immaterial  substances  are  ex- 
isting things,"  which  may  truly  be  inferred  from  the  con- 
rertend.  The  proposition  0,  then,  is  only  to  be  converted 
by  this  exceptional  method  of  negation. 

Another  process  of  conversion  can  be  applied  to  the 
proposition  A,  and  is  known  as  conversion  by  contra- 
position.  From  "  all  metals  are  elements,"  it  neces- 
sarily follows  that  "all  not-elements  are  not  metals.* 
If  this  be  not  at  the  first  moment~apparent,  a  little  re- 
flection  will  render  it  so,  and  from  fig.  5  we  see  that  if 
ill  the  metals  be  among  the  elements,  whatever  is  not  ele* 

6-a 


•4        CONVERSION  OF  PROPOSITIONS,    [LK» 

ment,  or  outside  the  circle  of  elements,  must    also   be 
outside  the  circle  of  metals.   We  may  also  prove  the  troth 

Fig.  5- 


•f  the  contrapositive  proposition  in  this  way,  if  we  may 
anticipate  the  contents  of  Lesson  xxin.:— If  what  is  not 
element  should  be  metal,  then  it  must  be  an  element  by 
the  original  proposition,  or  it  must  be  at  once  an  ele- 
ment and  not  an  element ;  which  is  impossible  accord- 
ing to  the  Primary  Laws  of  Thought  (Lesson  XIV.),  since 
nothing  can  both  have  and  not  have  the  same  property. 
It  follows  that  what  is  not-element  must  be  not-metal 

Mistakes  may  readily  be  committed  in  contrapositive 
conversion,  from  a  cause  which  will  be  more  apparent  in 
Lesson  XXII.  We  are  very  liable  to  infer  from  a  pro- 
position of  the  form  "all  metals  are  elements,"  that  all 
Hot-metals  are  not-tUments,  which  is  not  only  a  false 
statement  in  itself,  but  is  not  in  the  least  warranted  by 
the  original  proposition.  In  fig.  5,  it  is  apparent  that 
because  a  thing  lies  outside  the  circle  of  metals,  it  does 
not  necessarily  lie  outside  the  circle  of  elements,  which  is 
wider  than  that  of  metals.  Nevertheless  the  mistake  is 
often  made  in  common  life,  and  the  reader  will  do  well 
to  remember  that  the  process  of  conversion  by  contra- 
position consists  only  in  taking  the  negative  of  the  pre- 
dicate of  the  proposition  A,  as  a  new  subject,  and  affirm- 
ing of  it  universally  the  negative  of  the  old  subject. 


t}        AND  IMMEDIATE  INFERENCE.  83 

Contrapositive  conversion  cannot  be  applied  to  UM 
particular  propositions  I  and  0  at  all,  nor  to  the  propo- 
sition E,  in  that  form ;  but  we  may  change  B  into  A  by 
attaching  the  negation  to  the  predicate,  and  then  the 
process  can  be  applied.  Thus  "no  men  are  perfect" 
may  be  changed  into  "all  men  are  not-perfect,"  Le. 
'are  imperfect,"  and  then  we  infer  by  contraposition 
"  all  not-imperfect  beings  are  not-men."  But  not-im- 
perfect is  really  the  same  as  perfect,  so  that  our  new 
proposition  is  really  equivalent  to  "  all  perfect  beings  are 
not  men,"  or  "  no  perfect  beings  are  men,"  (B)  the  sim- 
ple converse  of  the  original  proposition. 

There  remain  to  be  described  certain  deductions 
which  may  be  drawn  from  a  proposition  without  convert- 
ing its  terms.  They  may  be  called  immediate  inferences, 
and  have  been  very  clearly  described  by  Archbishop 
Thomson  in  his  "Outline  of  the  Necessary  Laws  of 
Thought  "(pp.  156,  &c.). 

Immediate  Inference  by  Privative  Conception  consists 
in  passing  from  any  affirmative  proposition  to  a  negative 
proposition  implied  in  it,  or  equivalent  to  it,  or  vice  versa, 
in  passing  from  a  negative  proposition  to  its  correspond- 
ing affirmative. 

The  following  table  contains  a  proposition  of  each 
kind  changed  by  privative  conception  into  an  equivalent 
proposition : 

{A   all  metals  are  elements. 
B   no  metals  are  compounds. 
{E   no  men  are  perfect 
A   all  men  are  imperfect 
1 1    some  men  are  trustworthy. 
(0   some  men  are  not  untrustworthy. 
JO   some  men  are  not  trustworthy. 
(1    some  men  are  untrustworthy. 
The  truth  of  any  of  the  above  can  be  clearly  illustrated 


16       CONVERSION  OF  PROPOSITIONS^    [LB8* 

by  diagrams ;  thus  it  will  be  apparent  that  if  the  whole 
circle  of  metals  lies  inside  the  circle  of  elements,  no  part 
can  lie  outside  of  that  circle  or  among  the  compounds. 
Any  of  the  above  propositions  may  be  converted,  but  the 
results  will  generally  be  such  as  we  have  already  ob- 
tained. Thus  the  simple  converse  of  "  no  metals  are 
compounds"  is  "  no  compounds  are  metals,"  or  "  no  not- 
elements  are  metals,"  the  contrapositive  of  "  all  .metals 
are  elements."  From  the  last  example  we  get  also  by 
simple  conversion  "  some  untrustworthy  beings  are  men,11 
which  is  obviously  the  converse  by  negation,  as  before 
explained.  Applying  this  kind  of  conversion  to  "  some 
men  are  not  untrustworthy,"  we  have  "  some  not-untrust- 
worthy beings  are  men."  Lastly,  from  "all  men  arc 
imperfect"  we  may  obtain  through  conversion  by  limita- 
tion, "  some  imperfect  beings  are  men." 

Immediate  Inference  by  added  determinants  consists 
in  joining  some  adjective  or  similar  qualification  both  to 
tne  subject  and  predicate  of  a  proposition,  so  as  to  ren- 
der the  meaning  of  each  term  narrower  or  better  detei'- 
mined.  Provided  that  no  other  alteration  is  made  the 
truth  of  the  new  proposition  necessarily  follows  from  the 
truth  of  the  original  in  almost  all  cases. 

From  "all  metals  are  elements,"  we  may  thus  infer 
that  "all  very  heavy  metals  are  very  heavy  elements." 
From  "  a  comet  is  a  material  body"  we  infer  "  a  visible 
comet  is  a  visible  material  body."  But  if  we  apply  this 
kind  of  inference  too  boldly  we  may  meet  with  fallacious 
and  absurd  results.  Thus,  from  "all  kings  are  men," 
we  might  infer  "  all  incompetent  kings  are  incompetent 
men ;"  but  it  does  not  at  all  follow  that  those  who  art 
incompetent  as  kings  would  be  incompetent  in  othei 
positions.  In  this  case  and  many  others  the  qualifying 
adjective  is  liable  to  bear  different  meanings  in  the  sub- 
ject and  predicate ;  but  the  inference  will  only  be  true  a/ 


X.]        AND  IMMEDIATE  INFERENCE.  9) 

necessity  when  the  meaning  is  exactly  the  same  In  each 
case.  With  comparative  terms  this  kind  of  inference 
prill  seldom  be  applicable;  thus  from  "a  cottage  is  a 
building,"  we  cannot  infer  "a  huge  cottage  is  a  hug* 
building,"  since  a  cottage  may  be  large  when  compared 
irith  other  cottages,  but  not  with  buildings  generally. 

Immediate  Inference  by  Complex  Conception  is  closely 
iimilar  to  the  last,  and  consists  in  employing  the  subject 
and  predicate  of  a  proposition  as  parts  of  a  more  com- 
plex conception.  From  "  all  metals  are  elements,"  I  can 
pass  to  "  a  mixture  of  metals  is  a  mixture  of  elements." 
From  "  a  horse  is  a  quadruped"  I  infer  "  the  skeleton  of 
a  horse  is  the  skeleton  of  a  quadruped."  But  here  again 
the  reader  must  beware  of  applying  the  process  where 
the  new  complex  conception  has  a  different  meaning  in 
the  subject  and  predicate.  Thus,  from  "  all  Protestants 
are  Christians,"  it  does  not  follow  that  "a  majority  of 
Protestants  are  a  majority  of  Christians,"  nor  that  "the 
most  excellent  of  the  Protestants  is  the  most  excellent  of 
the  Christians." 

The  student  is  recommended  to  render  himself  fami- 
liar with  all  the  transformations  of  propositions,  or  im- 
mediate inferences  described  in  this  lesson ;  and  copious 
examples  are  furnished  for  the  purpose.  It  is  a  good 
exercise  to  throw  the  same  proposition  through  a  series 
of  changes,  so  that  it  comes  out  in  its  original  form  at 
last,  and  thus  proves  the  truth  of  all  the  intermediate 
changes  ;  but  should  conversion  by  limitation  have  beec 
tued,  the  original  universal  proposition  cannot  be  re- 
gained, but  only  the  particular  proposition  corresponding 
io  it 

On  Immediate  Inference,  Archbishop  Thomsons 
Outline  of  the  Laws  of  Thought,  §§  85— 93. 


LESSON  XL 
LOGICAL  ANALYSIS  OF  SENTENCE* 

PROPOSITIONS  as  they  are  usually  to  be  found  in  writ 
ten  or  spoken  compositions  seldom  exhibit  the  simple 
form,  the  conjunction  of  a  subject,  copula,  and  predicate, 
whirh  we  have  seen  to  be  the  proper  logical  construction. 
Not  only  is  the  copula  often  confused  with  the  predicate, 
but  several  propositions  may  be  combined  into  one  gram 
matical  sentence.  For  a  full  account  of  the  analysis 
of  sentences  I  shall  refer  to  several  excellent  little  works 
devoted  to  the  subject ;  but  I  will  here  attempt  to  give  a 
sketch  of  the  various  ways  in  which  a  sentence  may  be 
constructed. 

So  often  is  the  copula  united  to  the  predicate  in 
oidinary  language,  that  the  grammarian  treats  the  propo- 
sition as  composed  of  only  two  parts,  the  subject  and 
predicate,  or  verb.  Thus  the  proposition,  "The  sun 
rises,"  apparently  contains  nothing  but  a  subject  "the 
sun,"  and  a  predicate  "rises;"  but  the  proposition  is 
really  equivalent  to  "the  sun  is  rising,"  in  which  the 
copula  is  distinctly  shown.  We  shall,  therefore,  con- 
sider the  verb  or  grammatical  predicate  as  containing  both 
copula  and  logical  predicate.  In  Latin  one  single  word 
may  combine  all  the  three  parts  of  Che  proposition,  as  in 
turn*  "  I  am  ?  and  the  celebrated  exclamation  of  Caesar 
Vtni,  vuK,  vici,  "  I  came,  I  saw,  I  conquered,"  contain! 
three  distinct  and  complete  propositions  in  three  words, 
These  peculiar  cases  only  arise,  however,  from  the  para 
if  the  proposition  having  been  blended  together  and  dis- 


LESS.  XI.]     ANALYSIS  OF  SENTENCES.  89 

guised  in  one  word  ;  and  in  the  Latin  sum,  the  letter  m 
is  a  relic  of  the  pronoun  me,  which  is  the  real  subject  erf 
the  proposition.  If  we  had  a  perfect  acquaintance  with 
the  Grammar  of  any  language  it  would  probably  not  con- 
tradict the  logical  view  of  a  sentence,  but  would  perhaps 
sxplain  how  the  several  parts  of  the  complete  proposition 
*ad  become  blended  and  apparently  lost,  just  as  the 
words  will  and  not  are  blended  in  the  colloquial  "  I  wont.*5 
A  grammatical  sentence  may  contain  any  number  of 
distinct  propositions,  which  admit  of  being  separated  but 
which  are  combined  together  for  the  sake  of  brevity.  .In 
the  sentence, 

"Art  is  long  and  Time  is  fleeting," 

there  are  two  distinct  subjects,  Art  and  Time,  and  two 
predicates,  "long"  and  "fleeting,"  so  that  we  have  simply 
two  propositions  connected  by  the  conjunction  and.  We 
may  have  however  several  distinct  subjects  with  one  and 
the  same  predicate  ;  as  in 

"  Thirty  days  hath  September, 
April,  June,  and  November. " 

In  this  well-known  couplet  the  predicate  "  having 
thirty  days  "  is  placed  first  for  the  sake  of  emphasis,  and 
there  are  four  subjects,  September,  April,  &c.,  of  each  of 
which  it  is  affirmed.  Hence  these  lines  really  contain  four 
distinct  propositions. 

Again ,  there  may  be  one  subject  with  a  plurality  of 
predicates,  so  that  several  different  propositions  are  as- 
serted without  the  repetition  of  the  subject  and  copula. 
Thus  the  sentence 

"Nitrogen  is  a  colourless,  tasteless,  inodorous  gas, 
•lightly  lighter  than  air,"  contains  one  subject  only,  Ni* 
bvgen,  but  four  or  five  predicates ;  it  is  plainly  equiva- 
lent  to  "Nitrogen  is  colourless,"  "Nitrogen  is  tasteless," 
11  Nitrogen  is  a  gas,"  and  so  on. 

Lastly,  we  may  have   several    subjects  and 


90  LOGICAL  ANALYSIS  [L 

predicates  all  combined  in  the  same  sentence,  and  with 
only  one  copula,  so  that  each  predicate  is  asserted  ol 
each  subject ;  and  a  great  number  of  distinct  propositions 
are  condensed  into  one  brief  sentence.  Thus  in  the  sen- 
tence, "  Iron,  Copper,  Lead  and  Zinc  are  abundant,  cheap 
and  useful  metals,*"  we  have  evidently  four  subjects,  and 
we  may  be  said  to  have  four  predicates,  "abundant," 
44 cheap,"  "useful,"  and  "metal"  As  there  is  nothing  to 
prevent  our  applying  each  predicate  to  each  subject  the 
sentence  really  contains  16  distinct  propositions  in  only 
1 1  words  ;  thus  "  Iron  is  abundant,"  "  Iron  is  cheap,' 
"Copper  is  abundant,"  "Copper  is  cheap,"  and  soon. 
In  the  curious  sentence, — 

'*  Hearts,  tongues,  figures,  scribes,  bards,  poets,  can- 
not think,  speak,  cast,  write,  sing,  number,  his  love  to 
Antony*,"  Shakspeare  has  united  six  subjects  and  six 
predicates,  or  verbs,  so  that  there  are,  strictly  speaking, 
six  times  six  or  thirty-six  propositions. 

In  all  the  cases  above  noticed  the  sentence  is  said  to 
be  compound,  and  the  distinct  propositions  combined 
together  are  said  to  be  coordinate  with  each  other,  that  is 
of  the  same  order  or  kind,  because  they  do  not  depend 
upon  each  other,  or  in  any  way  affect  each  other's  truth. 
The  abundance,  cheapness,  or  utility  of  iron  need  not 
be  stated  in  the  same  sentence  with  the  qualities  of  cop- 
per, lead  or  zinc  ;  but  as  the  predicates  happen  to  be  the 
same,  considerable  trouble  in  speaking  or  writing  is 
saved  by  putting  as  many  subjects  as  possible  to  the 
same  set  of  predicates.  It  is  truly  said  that  brevity 
ts  the  soul  of  wit,  and  one  of  the  great  arts  of  compo- 
sition consists  in  condensing  as  many  statements  as 
possible  into  the  fewest  words,  so  long  as  the  meaning  ii 
tot  confused  thereby. 

•  Antony  an*  CUopatra,  Act  IIL  Sc.  t. 


M.]  OF  SENTENCES.  91 

Propositions  are  however  combined  in  a  totally  dif« 
ferent  manner  when  one  proposition  forms  a  part  of  the 
subject  or  predicate  of  the  other.  Thus  in  the  sen- 
tence, "The  man  who  is  upright  need  not  feai  accusa- 
tion," there  are  two  verbs,  and  two  propositions,  but  one 
of  these  only  describes  the  subject  of  the  other;  "who 
is  upright "  evidently  restricts  the  application  of  the  pre- 
dicate "  need  not  fear  accusation  "  to  a  part  of  the  class 
"  man. "  The  meaning  of  the  whole  sentence  might  be 
expressed  in  the  form 

"  The  upright  man  need  not  fear  accusation. " 
And  it  is  clearly  seen  that  the  clause  or  apparent  propo- 
sition is  substituted  for  an  adjective.  Such  a  clause  or 
proposition  is  called  subordinate,  because  it  merely  as- 
sists in  the  formation  of  the  principal  sentence,  and  has 
no  meaning  apart  from  it ;  and  any  sentence  containing 
a  subordinate  clause  is  said  to  be  complex.  Almost  any 
part  of  a  sentence  may  thus  be  replaced  by  a  subordinate 
clause.  Thus  in  "Oxygen  and  Nitrogen  are  the  gases 
which  form  the  largest  part  of  the  atmosphere,"  there  is  a 
subordinate  clause  making  part  of  the  predicate,  and  the 
meaning  might  be  expressed  nearly  as  well  in  this  way, 
"  Oxygen  and  Nitrogen  are  the  gases  forming  the  largest 
part  of  the  atmosphere." 

In  the  case  of  a  modal  proposition  (see  p.  69),  or  one 
which  states  the  manner  in  which  the  predicate  belongs 
to  the  subject,  the  mode  may  be  expressed  either  by  an 
adverb,  or  by  a  subordinate  clause.  "As  a  man  lives  so 
he  dies"  is  such  a  proposition;  for  it  means,  "a  man 
dies  as  he  lives,"  and  "as  he  lives"  is  equivalent  to  an 
adverb ;  if  he  lives  well,  he  dies  well ;  if  he  lives  badly, 
he  lies  badly.  Adverbs  or  adverbial  clauses  may  also 
specify  the  time,  place,  or  any  other  circumstance  con 
ccrned  in  the  truth  of  the  main  proposition. 

Assuming  the  reader  to  be  acquainted  with  the  gram 


92  LOGICAL  ANALYSTS  [LES& 

matical  terms  used,  we  may  thus  state  the  parts  of  whicl 

the  most  complex  sentence  must  consist 
The  antject  may  consist  of — 
I      A  noun ;  as  in  "  The  Queen  reigns." 

2.  A  pronoun  ;  as  in  "  She  reigns." 

3.  An  adjective  converted  into  a  noun  ;  as  in  "  H'kth 
are  civilized." 

4.  A  gerund ;  as  "  Seeing  is  believing  " 

5.  An  infinitive ;  as  "  To  see  is  to  believe." 

6.  A  subordinate  clause ;  as  "  Who  falls  from  virtut 
is  lost" 

The  subject  may  be  qualified  or  restricted  by  combin 
ing  with  it  an  attribute  which  may  be  expressed  in  any  ol 
the  following  ways : 

1.  An  adjective;  as,  "Fresh  air  is  wholesome." 

2.  A  participle ;  as  "  Falling  stars  are  often  seen." 

3.  A  noun  used  as  an  adjective ;  as  "  Iron  ships  are 
now  much  employed." 

4.  A  noun  and  preposition  ;  as  "ships  of  iron  are  now 
much  employed." 

5.  A  possessive  case;  as  " Chathants  son  was  the 
great  minister  Pitt." 

6.  A  noun  in  apposition ;  as  "  The  Metropolis  London 
is  the  most  populous  of  cities." 

7.  A  gerund  or  dative  infinitive ;  as,  "  The  desire  to  ?o 
abroad  is  common  in  Englishmen." 

The  predicate  consists  almost  always  of  a  verb,  which 
often  has  some  object  or  qualifying  words;  thus  it  may 
be— 

1.  A  simple  tense  of  a  complete  verb ;  as  "  The  sun 

rite" 

2.  A  compound  tense ;  as  "  The  sun  has  risen? 

\.  An  incomplete  verb  and  complement;  as  "Thf 
M*  appMrs  rough." 


W.J  OF  SENTENCES.  93 

4.  The  verb  "to  be"  and  an  adjective:  as  "Time  i. 
fluting? 

5.  A  verb  with  an  object ;  as  "  Warmth  melts  ice? 

6.  A  verb  with  an  adverbial;  as   "The  snow  fall* 
tkukly? 

The  object  of  a  verb  is  usually  a  noun  or  pronoun, 
but  any  other  of  the  six  kinds  of  expressions  which  may 
serve  as  a  subject  may  also  serve  as  an  object. 

The  adverbial  qualifying  a  verb  and  expressing  the 
manner,  time,  place,  or  other  circumstance  affecting  the 
proposition  may  be— 

1.  An  adverb ;  as  "  The  days  pass  slowly." 

2.  A  noun  and  preposition ;  as  "  The  resolution  was 
passed  by  a  large  majority" 

3.  An  absolute  phrase ;  as  "  The  snow  melts,  the  sun 
having  risen." 

4.  A  dative  infinitive ;  as  "  She  stoops  to  conquer? 

5.  Any  phrase  equivalent  to  an  adverb ;  as  "  The  divi- 
dends are  paid  twice  a  year." 

Various  modes  of  exhibiting  the  construction  of  sen 
tences  by  symbols  and  names  for  the  several  parts  have 
been  invented ;  but  I  belieye  that  by  far  the  simplest  and 
most  efficient  mode  is  to  exhibit  the  construction  in  the 
form  of  a  diagram.  Any  two  or  more  parts  of  a. sentence 
>vhich  are  co-ordinate  with  each  other,  or  bear  the  sarm 
relation  to  any  other  part,  are  written  alongside  eact 
jther,  and  coupled  together  by  a  bracket;  thus  the  du 
41  am, — 

Iron        i  (   abundant, 

Copper    I  I   cheap, 

Lead       (    "*    |   useful 

Zinc        I  I  metals, 

shows   that  there  art-  four  co-ordinate  subject* 


94  LOGICAL  ANALYSIS  [Lisa 

and  four  coordinate  predicates  in  the  example  previous!) 
taken, 

Whenever  one  part  of  a  sentence  is  subordinate  to 
another  part  it  may  be  connected  with  it  by  a  line  drawi 
A  any  convenient  direction.  Thus  the  analysis  of  the 
Allowing  sentence  is  readily  shown  by  the  diagram  belov 
t  :— 

"  No  one  who  is  a  lover  of  money,  a  lover  of  pleasure, 
and  a  lover  of  glory,  is  likewise  a  lover  of  mankind  ;  but 
oaly  he  who  is  a  lover  of  virtue." 

t  a  lover  of  money, 
who  is  /  a  lover  of  pleasure, 

|         (  a  lover  of  glory. 
one  is  not  j  a  lovef  of  mankin^ 
he  only  is  ) 

I 
who  is  a  lover  of  virtue. 

?Ve  see  that  the  sentence  is  both  compound  and  com- 
plex, that  is  to  say  it  contains  two  principal  coordinate 
propositions  with  a  common  predicate,  "  a  lover  of  man- 
kind" The  first  proposition  is  negative  and  its  subject  is 
described  by  three  subordinate  clauses,  while  the  second 
proposition  is  affirmative  and  has  one  subordinate  clause. 

I  conclude  this  somewhat  lengthy  lesson  with  the 
analysis  of  a  few  sentences,  of  which  the  first  consist! 
rf  some  remarkably  complex  lines  from  a  poem  of  Bur 
bidge: 

"  He  who  metes,  as  we  should  mete, 
Could  we  His  insight  use,  shall  most  approve, 
Not  that  which  fills  most  space  in  earthly  eyes, 
But  what — though  Time  scarce  note  it  as  he  ; 
Fills,  like  this  little  daisy  at  my  feet, 
Its  function  best  of  diligence  in  love." 


«,]  OF  SENTENCES.  gft 

which  fills  most  space  in  earthly  eyt* 

(  not  that 
He  shaU  most  approve  }  bu(  wfaa 


1     | 


,  -  -  - 

who  metes  its  function  of    like  this  littlf 

as  we  should  mete         diligence  in        daisy  at  my 

|  love  feet, 

mid  we  His  insight  use.  ^h  fime  scan*  aote  it 

as  he  flies. 
"  Most  sweet  it  is  with  unuplifted  eyes 

To  pace  the  ground,  if  path  there  be  or  none, 
While  a  fair  region  round  the  traveller  lies 

Which  he  forbears  again  to  look  upon  ; 
Pleased  rather  with  some  soft  ideal  scene, 
The  work  of  fancy,  or  some  happy  tone 
Of  meditation  slipping  in  between, 
The  beauty  coming,  and  the  beauty  gone." 

WORDSWORTH 
It  is  most  sweet 
f 
To  pace  the  ground  _ 

with  unuplifted  if  path  while  a  fair  region 

^es  there  j  be  round  the        I 

(  or  none        traveller  lies 


r&ch  (region)  he  (the  traveller)  forbears  to  look  upon 

{some  soft  ideal  scene 
the  work  of  fancy 
or  some  happy  tone  of  meditation 


slipping  in  between  the  beauty  coming 

and  the  beauty  gone. 
ID  the  above  sentence  there  is  evidently  one  rubjetf 


96  LOGICAL  ANALYSIS  [LESS. 

*•  to  pace  the  ground,"  which  by  means  ol  the  pronoun  it 
is  connected  with  the  predicate  most  sweet.  The  main 
part  ot  the  sentence  however  consists  of  three  adverbials, 
expressing  the  manner  and  surrounding  circumstances 
and  the  third  adverbial  is  developed  in  a  very  complicated 
manner.  The  sentence  is  not  compound,  but  is  complei 
on  account  of  four  subordinate  propositions. 

In  the  following  sentence  there  is  strictly  but  on< 
principal  proposition,  "  We  find,"  but  this  is  only  a  mode 
of  introducing  the  true  purport  of  the  sentence,  "  the  two 
classes  of  intellectual  operations  have  much  that  is  differ 
ent,  much  that  is  common." 

ft  When  the  notions  with  which  men  are  conversant  in 
the  common  course  of  life,  which  give  meaning  to  theii 
familiar  language  and  which  give  employment  to  theii 
hourly  thoughts,  are  compared  with  the  ideas  on  which 
exact  science  is  founded,  we  find,  that  the  two  classes  of 
intellectual  operations  have  much  that  is  different,  much 
that  is  common." 
we  find — that  the  two  classes  (*  f) 

I  of  intellectual      j  much  that  is  different 

operations  have  (  much  that  is  common 

When  the  notions  *  are  compared . 

with  which    which  give    which  give       with  the  ideas  f 
men  are        meaning        employ-  j 

conversant    to  their          ment  to  on  w^ch 

in  the  familiar         their  hourly      exact  science  is 

common        language       thoughts  founded, 

course 
of  life 

Here  the  two  classes  form  a  collective  term,  and  hare 
two  coordinate  predicates  rendering  the  sentence  so  far  a 
compound  one.  The  greater  part  of  the  sentence,  how- 
ever,  consists  of  a  complicated  subordinate  sentence  of 


XL]  OF  SENTENCES.  97 

the  nature  of  an  adverbial,  expressing  the  time  or  occa- 
sion when  this  is  found  to  be  the  case. 

As  a  last  example  we  take  the  sentence  given  below: — 
"The  law  of  gravitation,  the  most  universal  truth  at 
which  human  reason  has  yet  arrived,  expresses  not  merely 
the  general  fact  of  the  mutual  attraction  of  all  matter;  not 
merely  the  vague  statement  that  its  influence  decreases  as 
the  distance  increases,  but  the  exact  numerical  rate  at 
which  that  decrease  takes  place  ;  so  that  when  its  amount 
is  known  at  any  one  distance  it  may  be  exactly  calculated 
for  any  other." 

at  which  human  reason  has  yet  arrired 
the  most  universal  truth 
The  law  of  gravitation  expresses 


not  merely  the 
general  fact 

of  the  mutual 
attraction  of  all 
matter 

not  merely  the 
vague  statement 

that  its  influence 
decreases 

as  the  distance 
increases 

butt! 
numei 

at  whi 
decrea 
pk 

te  exact 
•ical  rate 

ch  that 
se  takes 
tee 

BO  that  its  amount  may  be  calculated  for  any  other  dis- 

|  [tancc 

when  it  is  known  at  any  one  distance. 

W.  S.  Dalgleish's  Grammatical  Analysis,  or 

J.  D.  Morell's  Analysis  of  Sentences. 

Alex.  Bain's  English  Composition  and  RM*- 

torie,  pp.  91— 1 17,  treats  of  construction  of 

sentences. 


LESSON   XII. 


THE   PREDICABLES,    DIVISION,   AND 
DEFINITION 

IT  is  desirable  that  the  reader,  before  proceeding  further, 
should  acquire  an  exact  comprehension  of  the  meaning  of 
certain  logical  terms  which  are  known  as  the  Predicables, 
meaning  the  kinds  of  terms  or  attributes  which  can  always 
be  predicated  of  any  subject  These  terms  are  five  in 
number ;  genus,  species,  difference,  property,  and  acci- 
dent ;  and  when  properly  employed  are  of  exceeding  use 
and  importance  in  logical  science.  It  would  neither  be 
possible  nor  desirable  in  this  work  to  attempt  to  give  any 
idea  of  the  various  and  subtle  meanings  which  have  been 
attributed  to  the  predicables  by  ancient  writers,  and  the 
most  simple  and  useful  view  of  the  subject  is  what  alone 
can  be  given  here. 

Any  class  of  things  may  be  called  a  genus  (Greek 
y«W,  race  or  kind),  if  it  be  regarded  as  made  up  of  two 
or  more  species.  "  Element"  is  a  genus  when  we  con- 
sider it  as  divided  into  the  two  species  "metallic  and 
non-metallic."  Triangle  is  a  genus  as  regards  the  species 
acute-angled,  right-angled,  and  obtuse-angled. 

On  the  other  hand,  a  species  is  any  class  which  is  re- 
garded as  forming  part  of  the  next  larger  class,  so  that 
the  terms  genus  and  species  are  relative  to  each  othei, 
the  genus  being  the  larger  class  which  is  divided,  and  the 
species  the  two  or  more  smaller  classes  into  which  the 
genus  is  divided. 

It  is  indispensable,  however,  to  regard  these  expres- 
sions in  the  double  meaning  of  extension  and  intension 


LESS,  xii  ]     THE  PREDICABLES,  ETC.  & 

From  the  explanation  of  these  different  meanings  in 
Lesson  V.  it  will  be  apparent  that  the  extent  of  a  genus 
or  species  is  simply  the  number  of  individuals  included 
in  it,  and  there  will  always  be  fewer  individuals  in  the 
species  than  in  the  genus.  In  extent  the  genus  book  in- 
cludes all  books  of  whatever  size,  language,  or  contents  j 
if  divided  in  respect  to  size  the  species  of  book  are  folio, 
quarto,  octavo,  duodecimo,  &c. ;  and,  of  course,  each  oi 
these  species  contains  much  fewer  individual  books  than 
the  whole  genus. 

In  Intension  the  genus  means,  not  the  individual 
things  contained  in  it,  but  the  sum  of  the  qualities  com- 
mon to  all  those  things,  and  sufficient  to  mark  them  out 
clearly  from  other  classes.  The  species  similarly  means 
the  sum  of  the  qualities  common  to  all  the  individuals 
forming  part  of  the  genus,  and  sufficient  to  mark  them  out 
from  the  rest  of  the  genus,  as  well  as  from  all  other  things. 
It  is  evident,  therefore,  that  there  must  be  more  qualities 
implied  in  the  meaning  of  the  species  than  of  the  genus, 
for  the  species  must  contain  all  the  qualities  of  the  genus, 
as  well  as  a  certain  additional  quality  or  qualities  by 
which  the  several  species  are  distinguished  from  each 
other.  Now  these  additional  qualities  form  the  difference, 
which  may  be  defined  as  the  quality  or  sum  of  qualities 
which  mark  out  one  part  of  a  genus  from  the  other  part  ot 
parts.  The  difference  (Latin  differentia,  Greek  flta- 
<£opd)  cannot  have  any  meaning  except  in  intension; 
and  when  we  use  all  the  terms  wholly  in  intension  we  may 
say  that  the  difference  added  to  the  genus  makes  the  species. 
Thus  if  "  building"  be  the  genus,  and  we  add  the  differ- 
ence "  used  for  a  dwelling,"  we  get  the  species  "  house. * 
If  we  take  "triangle"  as  the  genus,  it  means  the  sum  ol 
the  qualities  of  "  three-sided  rectilineal  figure ;"  if  we  add 
the  quality  of  "having  two  sides  equal,"  we  obtain  the 
species  "  isosceles  triangle." 

7—2 


too      THE  PREDICABLES,  DIVISION,       [] 

It  will  easily  be  seen  that  the  same  class  oi  thing* 
may  be  both  a  genus  and  a  species  at  the  same  time,  ao» 
cording  as  we  regard  it  as  divided  into  smaller  classes  of 
forming  part  of  a  larger  class.  Thus  triangle,  which  if 
i  genus  as  regards  isosceles  triangle,  is  a  species  as  ie- 
jards  right-Ikied  geometrical  figures.  House  is  a  species 
Df  building,  but  a  .genus  with  respect  to  mansion,  cottage, 
villa,  or  other  kinds  of  houses.  We  may,  in  fact,  have  an 
almost  interminable  chain  of  genera  and  species,  each 
class  being  a  species  of  the  class  next  above  it,  and  a 
genus  as  regards  that  next  below.  Thus  the  genus  Bri- 
tish subject  has  the  species  Born  in  the  United  Kingdom, 
Colonial-born,  and  Naturalised.  Each  of  these  becomes 
a  genus  as  regards  the  species  male  and  female;  each 
species  again  may  be  divided  into  adult  and  minor,  edu- 
cated, uneducated,  employed  in  some  occupation  or  un- 
employed, self-maintaining,  maintained  by  friends,  or 
pauper;  and  so  on.  The  subdivision  may  thus  proceed 
until  we  reach  a  class  of  so  restricted  extent,  that  it 
cannot  be  divided  except  into  individuals ;  in  this  case 
the  species  is  called  the  lowest  species  or  Inflma  species. 
All  the  intermediate  genera  and  species  of  the  chain  are 
called  subaltern  (Latin  sub,  under,  and  alter,  the  other  of 
two),  because  they  stand  one  under  the  other.  If  there  be 
a  genus  which  is  not  regarded  as  a  species,  that  is  as 
part  of  any  higher  genus,  it  is  called  the  summum  genus, 
the  highest  genus,  or  genus  generalissimum,  the  most 
general  genus.  It  is  questionable  whether  we  can  thus 
set  any  limit  to  the  chain  of  classes.  The  class  British 
tubject  is  certainly  not  an  absolute  summum  genus, 
rince  it  is  but  a  species  of  man,  which  is  a  species  of 
animal,  living  being,  inhabitant  of  the  earth,  substance, 
and  so  on.  If  there  were  any  real  summum  genus  it 
would  probably  be  "  Being,"  or  "  Thing,"  or  "  Object  con- 
ceivable ;"  but  we  mav  usefully  employ  the  term  to  signify 


Xii.?  AND  DEFINITION.  101 

the  highest  class  of  things  comprehended  in  any  science 
or  classification.  Thus  "material  substance"  is  the  sura- 
mum  genus  examined  in  the  science  of  chemistry;  "in- 
habitant of  the  United  Kingdom"  is  the  summum  genus 
enumerated  and  classified  in  the  British  census.  Logi- 
cal terms  are  only  a  species  of  words  or  phrases,  but  they 
are  the  summum  genus  as  regards  logic,  which  has  no- 
thing to  do  with  the  various  parts  of  speech  and  the 
relations  of  words,  syllables,  and  letters,  examined  bv 
grammarians. 

Several  very  useful  expressions  have  been  derived 
from  the  words  genus  and  species.  When  a  thing  is 
so  peculiar  and  unlike  other  things  that  it  cannot  easily 
be  brought  into  one  class  with  them,  it  is  said  to  be  sal 
generis,  or  of  its  own  genus ;  thus  the  rings  of  Saturn  are 
so  different  from  anything  else  among  the  heavenly  bodies 
that  they  may  fairly  be  called  sui  generis.  In  zoology, 
the  Ornithorhynchus,  or  Australian  Duck-bill,  the  Amphi- 
oxus,  and  some  other  animals,  are  so  peculiar  that  they 
may  be  called  sui  generis.  When  a  substance  is  the 
same  in  all  its  parts,  or  when  a  number  of  things  are  all 
alike,  we  say  that  they  are  homogeneous  (Greek  d/io*,  like, 
yt vos,  kind),  that  is  of  the  same  nature ;  otherwise  they 
may  be  called  heterogeneous  (Greek  ercpos,  other). 

It  is  necessary  to  distinguish  carefully  the  purely  lo- 
gical use  of  the  terms  genus  and  species  from  their  pecu- 
liar use  in  natural  history.  A  species  is  there  a  class 
of  plants  and  animals  supposed  to  have  descended  from 
common  parents,  and  to  be  the  narrowest  class  possessing 
a  fixed  form ;  the  genus  is  the  next  higher  class.  But  ii 
we  accept  Darwin's  theory  of  the  origin  of  species,  this 
definition  of  species  becomes  entirely  illusory,  since  dif- 
ferent genera  and  species  must  have  according  to  this 
theory  descended  from  common  parents.  The  species 
then  denotes  a  merely  arbitrary  amount  of  resemblance 


u»2        THE  PREDICABLES,  LI  VISION,       UZSS, 

which  naturalists  choose  to  fix  upon,  and  which  i  'i  not 
possible  to  define  more  exactly.  This  use  of  the  term, 
then,  has  no  connection  whatever  with  the  logical  use, 
according  to  which  any  class  of  things  whatever  is  a 
species,  provided  it  is  regarded  as  part  of  a  wider  class  oc 
genus. 

The  fourth  of  the  Predicables  is  Property  (Latin  fro* 
frium,  Greek  tdtoi/,  own),  which  it  is  hardly  possible  to 
define  in  a  manner  free  from  objection  and  difficulty,  but 
which  may  perhaps  be  best  described  as  any  quality 
which  is  common  to  the  whole  of  a  class,  but  is  not  neces- 
sary to  mark  out  that  class  from  other  classes.  Thus  it  is 
a  property  of  the  genus  "  triangle"  to  have  the  three  in- 
ternal angles  equal  to  two  right  angles;  this  is  a  very 
remarkable  circumstance,  which  is  always  true  of  tri- 
angles, but  it  is  not  made  a  part  of  the  genus,  or  is  not 
employed  in  defining  a  triangle,  because  the  possession  of 
three  straight  sides  is  a  sufficient  mark.  The  properties  of 
geometrical  figures  are  very  numerous ;  the  Second  Book 
of  Euclid  is  occupied  in  proving  a  few  properties  of  rect- 
angles ;  the  Third  Book  similarly  of  circles.  As  we  com- 
monly use  the  term  property  it  may  or  may  not  belong  to 
other  objects  as  well  as  those  in  question ;  some  of  the 
properties  of  the  circle  may  belong  also  to  the  ellipse; 
some  of  the  properties  of  man,  as  foi  instance  the  power 
of  memory,  or  of  anger,  may  belong  to  other  animals. 

Logicians  have  invented  various  subtle  divisions  of  pro- 
perties, but  it  will  be  sufficient  to  say  that  a  peculiar  pro- 
perty is  one  which  belongs  to  the  whole  of  a  class,  and  to 
that  class  only,  as  laughter  is  supposed  to  belong  only  »o 
mankind  ;  the  property  of  containing  the  greatest  space  in 
a  line  of  given  length  is  peculiar  to  circles.  When  a  pro- 
perty is  not  peculiar,  it  may  belong  to  other  classes  oi 
objects  as  well  as  that  of  which  it  is  called  the  property 
We  may  further  distinguish  the  Generic  Property,  or  thai 


xii.]  AND  DEFINITION  u>< 

which  belongs  to  the  whole  of  the  genus,  from  the 
Specific  Property,  which  belongs  to  the  whole  of  a  lowest 
species. 

Lastly,  an  accident  (Latin  atcidens,  Greek  <rvp$t$n- 
toc)  is  any  quality  which  may  indifferently  belong  01 
not  belong  to  a  class,  as  the  case  may  be,  without 
iffecting  the  other  qualities  of  the  class.  The  word 
means  that  which  falls  or  happens  by  chance,  and  has  no 
necessary  connection  with  the  nature  of  a  thing.  Thus 
the  absolute  size  of  a  triangle  is  a  pure  accident  as 
regards  its  geometrical  properties;  for  whether  the  side 
of  a  triangle  be  fa  of  an  inch  or  a  million  miles,  what- 
ever Euclid  proves  to  be  true  of  one  is  true  of  the  other. 
The  birthplace  of  a  man  is  an  accident  concerning  him,  as 
are  also  the  clothes  in  which  he  is  dressed,  the  position  in 
which  he  rests,  and  so  on.  Some  writers  distinguish  se- 
parable and  inseparable  accidents.  Thus  the  clothes  in 
which  a  man  is  dressed  is  a  separable  accident,  because 
they  can  be  changed,  as  can  also  his  position,  and  many 
other  circumstances;  but  his  birthplace,  his  height,  his 
Christian  name,  &c.,  are  inseparable  accidents,  because 
.hey  can  never  be  changed,  although  they  have  no  neces- 
sary or  important  relation  to  his  general  character. 

As  an  illustration  of  some  part  of  the  scheme  of  clas- 
sification described  under  the  name  of  Predicables,  I  may 
here  give,  as  is  usual  in  manuals  of  Logic,  the  Tree  ol 
Porphyry,  a  sort  of  example  of  classification  invented  by 
one  of  the  earliest  Greek  logicians,  named  Porphyrius. 
i  have  simplified  the  common  form  in  which  it  is  given 
by  translating  the  Latin  names  and  omitting  superfluous 
words. 

In  this  Tree  we  observe  a  succession  of  genera  aad 
species— Substance,  Body,  Living  Being,  Animal  and 
Man.  Of  these  Substance  is  the  summunt  genus,  because 
fc  is  not  regarded  as  a  species  of  any  higher  class ;  Mai 


104        THE  PREDICABLES,    DIVISION,     [LESS 

is  the  infiina  species,  because  it  is  a  class  not  divided  in- 
to any  lower  class,  but  only  into  individuals,  of  whom  it  is 


Socrates,  Plato,          and  others. 

usual  to  specify  Socrates  and  Plato.  Body,  Living  Being 
and  Animal  are  called  subaltern  genera  and  species,  be- 
cause each  is  a  species  as  regards  the  next  higher  genus, 
and  a  genus  as  regards  the  next  lower  species.  The 
qualities  implied  in  the  adjectives  Corporeal,  Animate, 
Sensible  (i.e.  capable  of  feeling)  and  Rational  are  the 
successive  differences  which  occasion  a  division  of  each 
genus  into  species.  It  will  be  evident  that  the  negative 
parts  of  the  genera,  namely  Incorporeal  Substance,  In 


XII.] 


AND  DEFINITION. 


105 


animate  Body,  &c.,  are  capable  of  subdivision,  which  has 
not  been  carried  out  in  order  to  avoid  confusing  the 
figure. 

LogicaLjliyisios  is  the  name  of  the  process  by  which 
we  distinguish  the  species  of  which  a  genus  is  composed. 
Thus  we  are  said  to  divide  the  genus  "  book "  when  we 
consider  it  as  made  up  of  the  groups  folio,  quarto,  octavo, 
duodecimo  books,  &c.,  and  the  size  of  the  books  is  in  this 
case  the  ground,  basis,  or  principle  of  division,  commonly 
called  the  Fundamentum  Divisionis.  In  order  that  a  quality 
Dr  circumstance  may  be  taken  as  the  basis  of  division,  it 
jnust  be  present  with  some  and  absent  with  others,  or 
must  vary  with  the  different  species  comprehended  in  the 
genus.  A  generic  property  of  course,  being  present  in  the 
whole  of  the  genus,  cannot  serve  for  the  purpose  of  divi- 
sion. Three  rules  may  be  laid  down  to  which  a  sound 
and  useful  division  must  conform: 

1.  The  constituent  species  must  exclude  each  other. 

2.  The  constituent  species   must  be  equal  when  add- 
ed together  to  the  genus. 

3.  The  division  must  be  founded  upon  one  principle 
or  basis. 

It  would  be  obviously  absurd  to  divide  books  into 
3*^"  folio,  quarto,  French,  German  and  dictionaries,  because 
these  species  overlap  each  other,  and  there  may  be  French 
or  German  dictionaries  which  happen  to  be  quarto  or 
folio  and  belong  to  three  different  species  at  once.  A 
division  of  this  kind  is  said  to  be  a  Cross  Division,  because 
there  is  more  than  one  principle  of  division,  and  the  seve- 
ral species  m  consequence  cross  each  other  and  produce 
confusion.  If  I  were  to  divide  rectilineal  figures  into  tri- 
angles, parallelograms,  rectangles  and  polygons  of  more 
than  four  sides,  I  should  commit  all  the  possible  faults  in 
one  division.  The  species  parallelogram  and  rectangle 
do  not  exclude  each  other,  since  all  rectangles  must  be 


io6      THE  PREDICABLES,  DIVISION, 

parallelograms ;  the  constituent  species  are  not  altogethei 
equal  to  the  genus  rectilineal  figure,  since  irregular  four« 
sided  figures  which  are  not  parallelograms  have  been 
omitted ;  and  there  are  three  principles  of  division,  namely 
the  number  of  sides,  the  directions  of  those  sides,  and  the 
angles  contained.  But  when  subdivision  is  employed, 
and  each  of  the  species  is  considered  as  a  genus  which 
may  be  subjected  to  a  further  separation,  a  new  principle 
of  division  may  and  in  fact  must  be  employed  each  time, 
Thus  I  can  divide  rectilineal  figures  according  to  the  three 
principles  mentioned  above : 

Rectilineal  Figure 

3  sides  4  sides  more  than  4  sides 

Triangle  Quadrilateral  Polygon 

with  parallel  sides  without  parallel 

Parallelogram  sides 

Trapezium. 

Here  the  principles  of  division  are  the  number  of  their 
sides,  and  in  the  case  of  four-sided  figures  their  paral- 
lelism. Triangles  do  not  admit  of  division  in  this  second 
respect  We  may  make  a  new  division  of  parallelograms, 
adopting  the  equality  of  sides  and  the  size  of  the  angles 
as  the  principles ;  thus  : 

Parallelogram 


adjoining  sides 
equal 

adjoining  sides 
not  equal 

right-                 not  right- 
ingled               angled 
Square               Rhombus 

right-               not  right- 
angled               angled 
Oblong          Rhomboid 

The  most  perfect  divisions  in  a  logical  point  of  view 
e  produced  by  continually  dividing  each  genus  into  twc 


XIL]  AND  DEFINITION.  i& 

species  by  a  difference,  of  which  an  example  has  been 
given  in  the  Tree  of  Porphyry.  This  process  is  callcc 
Dichotomy  (Greek  di^a,  in  two;  reuva,  to  cut):  it  is  also 
called  Exhaustive  Division  because  it  alwavs  of  necessity 
obeys  the  second  rule,  and  provides  a  place  tor  every 
possible  existing  thing.  By  a  Law  of  Thought  to  be  con- 
sidered in  the  next  Lesson,  every  thing  must  either  havt 
a  quality  or  not  have  it,  so  that  it  must  fall  into  one  or 
other  division  of  the  genus.  This  process  of  exhaustive 
division  will  be  shewn  to  have  considerable  importance  in 
Lesson  XXIII.,  but  in  practice  it  is  not  by  any  means 
always  necessary  or  convenient  It  would,  for  instance, 
produce  a  needlessly  long  classification  if  we  divided  rec- 
tilineal figures  thus  : 

Rectilineal  figure 

3-sided  not  3-sided 

Triangle  , 1 , 

4-sided  not  4-sided 

Quadrilateral 


5-sided  not  5-sided 

Pentagon  &c. 

As  we  know  beyond  all  doubt  that  every  figure  must 
have  3,  4,  5,  6,  or  more  sides,  and  no  figure  can  belong  to 
more  than  one  group,  it  is  much  better  at  once  to  enume- 
rate the  parts  as  Triangle,  Quadrilateral,  Pentagon,  Hexa- 
gon, &c.  Again,  it  would  be  very  awkward  if  we  divided 
the  counties  of  England  into  Middlesex  and  not-Middle- 
sex;  the  latter  into  Surrey  and  not- Surrey;  the  latter, 
again,  into  Kent  and  not- Kent  Dichotomy  is  useless, 
and  even  seems  absurd  in  these  cases,  because  we  can 
observe  the  rules  of  division  certainly  in  a  much  briefer 
division.  But  in  less  certain  branches  of  knowledge  our 
divisions  can  never  be  free  from  possible  oversight  unless 
they  proceed  by  dichotomy.  Thus,  if  we  divide  the  popula- 
tion of  the  world  into  three  branches,  Aryan,  Semitic,  and 


co8        THE  FRED/CABLES,  DIVISION,      (lES* 

Turanian,  some  race  might  ultimately  be  discovered  whici 
is  distinct  from  any  of  these,  and  for  which  no  place  ha* 
been  provided ;  but  had  we  proceeded  thus— 

Man 
Aryan  not-Aryan 


Semitic  not-Semitic 


Turanian  not-Turanian, 

it  is  evident  that  the  new  race  would  fall  into  the  last 
group,  which  is  neither  Aryan,  Semitic,  nor  Turanian.  All 
the  divisions  of  naturalists  are  liable  to  this  inconvenience, 
If  we  divide  Vertebrate  Animals  into  Mammalia,  Birds, 
Reptiles,  and  Fish,  it  may  any  time  happen  that  a  new 
form  is  discovered  which  belongs  to  none  of  these,  and 
therefore  upsets  the  division. 

A  further  precaution  required  in  Division  is  not  to 
proceed  from  a  high  or  wide  genus  at  once  to  a  low 
or  narrow  species,  or,  as  the  phrase  is,  divisio  turn  facia* 
saltum  (the  division  should  not  make  a  leap).  The 
species  should  always  be  those  of  the  proximate  or  next 
higher  genus ;  thus  it  would  obviously  be  inconvenient  to 
begin  by  dividing  geometrical  figures  into  those  which 
have  parallel  sides  and  those  which  have  not;  but  this 
principle  of  division  is  very  proper  when  applied  to  the 
proximate  genus. 

Logical  division  must  not  be  confused  with  physical 
division  or  Partition,  by  which  an  individual  object,  as  a 
tree,  is  regarded  as  composed  of  its  separate  parts,  root, 
trunk,  branches,  leaves,  &e.  There  is  even  a  third  and 
distinct  process,  called  Metaphysical  Division,  which  con- 
lists  in  regarding  a  thing  as  an  aggregate  of  qualities, 
and  separating  these  in  thought ;  as  when  we  discriminate 
the  form,  colour,  taste,  and  smell  of  an  orange. 

Closely  connected  with  the  subject  of  this  Lesson  if 


XIL]  AND  DEFINITION.  109 

the  process  of  Logical  Definition,  by  which  we  determine 
the  common  qualities  or  marks  of  the  objects  belonging 
to  any  given  class  of  objects.  We  must  give  in  a  defini- 
tion the  briefest  possible  statement  of  such  qualities  as 
•re  sufficient  to  distinguish  the  class  from  other  classes, 
and  determine  its  position  in  the  general  classification  ol 
conceptions.  Now  this  will  be  fulfilled  by  regarding  the 
class  as  a  species,  and  giving  the  proximate  genus  and 
the  difference.  The  word  genus  is  here  used  in  its  inten- 
sive meaning,  and  denotes  the  qualities  belonging  to  all 
of  the  genus,  and  sufficient  to  mark  them  out ;  and  as  the 
difference  marks  out  the  part  of  the  genus  in  question, 
we  get  a  perfect  definition  of  the  species  desired.  But  we 
should  be  careful  to  give  in  a  definition  no  superfluous 
marks ;  if  these  are  accidents  and  do  not  belong  to  the 
whole,  the  definition  will  be  improperly  narrowed,  as  if 
we  were  to  define  Quadrilateral  Figures  as  figures  with 
four  equal  sides ;  if  the  superfluous  marks  belong  to  all 
the  things  defined  they  are  Properties,  and  have  no  effect 
upon  the  definition  whatever.  Thus  if  I  define  parallelo- 
grams as  "  four-sided  rectilineal  figures,  with  the  opposite 
sides  equal  and  parallel,  and  the  opposite  angles  equal," 
I  have  added  two  properties,  the  equality  of  the  opposite 
sides  and  angles  which  necessarily  follow  from  the  paral- 
lelism of  the  sides,  and  only  add  to  the  complexity  of  the 
definition  without  rendering  it  more  precise. 
/^There  are  certain  rules  usually  given  in  logical  works 
-^  which  express  the  precautions  necessary  in  definition. 

1.  A  definition  should  state  the  essential  attributes  oj 
the  species  defined.    So  far  as  any  exact  meaning  can  be 
fiven  to  the  expression  "essential  attributes,"  it  means, 
Mjexplained  above,  the  proximate  genus  and  difference. 

2.  A  definition  must  not  contain  the  name  defined* 
For  the  purpose  of  the  definition  is  to  make  the  species 
known,  and  as  long  as  it  is  not  known  it  cannot  serve  tt 


no        THE  PREDICABLES,  DIVISION,     [LESS 

make  itself  known.  When  this  rule  is  not  observed,  them 
is  said  to  be  *  circulus  in  dejiniendo]  or  *  a  circle  in  defin- 
ing,' because  the  definition  brings  us  round  again  to  the 
very  word  from  which  we  started.  This  fault  will  usually 
be  committed  by  using  a  word  in  the  definition  which  is 
really  a  synonym  of  the  name  denned,  as  if  I  were  to 
define  "  Plant"  as  "an  organized  being  possessing  vege- 
tab*e  life,"  or  elements  as  simple  substances,  vegetable 
being  really  equivalent  to  plant,  and  simple  to  elementary. 
If  I  were  to  define  metals  as  "  substances  possessing  me- 
tallic lustre,"  I  should  either  commit  this  fault,  or  use  the 
term  metallic  lustre  in  a  sense  which  would  admit  other 
substances,  and  thus>  break  the  following  rule. 

3.  The  definition  must  be  exactly  equivalent  to  tlu 
species  defined,  that  is  to  say,  it  must  be  an  expression  the 
denotation  of  which  is  neither  narrower  nor  wider  than 
the  species,  so  as  to  include  exactly  the  same  objects. 
The  definition,  in  short,   must   denote  the  species,  the 
whole  species,  and  nothing  but  the  species,  and  this  may 
really  be  considered  a  description  of  what  a  definition  is. 

4.  A  definition  must  not  be  expressed  in  obscurejigura- 
tive  or  ambiguous  language.     In  other  words,  the  terms 
employed  in  the  definition  must  be  all  exactly  known, 
otherwise  the  purpose  of  the  definition,  to  make  us  ac- 
quainted with  the   sufficient   marks  of  the   species,   is 
obviously  defeated.     There  is  no  worse  logical  fault  than 
to  define  ignotum  per  ignotius,  the  unknown  by  the  still 
more  unknown.    Aristotle's  definition  of  the  soul  as  *  The 
Entelechy,  or  first  form  of  an  organized  body  which  has 
potential  life,'  certainly  seems  subject  to  this  objection. 

5.  And  lastly,  A  definition  must  not  be  negative  when 
U  can  be  affirmative.     This  rule  however  is  often  not 
applicable,  and  is  by  no  means  always  binding. 

Read  Mr  M  ifl  on  the  nature  of  Classification  and  th< 


ML]  AND  DEFINITION.  in 

five  Predicables,  System  of  Logic,  Book  I.  Chap 
VII.  For  ancient  Scholastic  Views  concerning  De 
finition,  see  Mansel's  Artis  Logica  Rudiment* 
(Aldrich),  App.  Note  C. 


LESSON   XIII. 

PASCAL  AND  DESCARTES  ON   METHOD. 

IT  may  be  doubted  whether  any  man  ever  possessed  a 
more  acute  and  perfect  intellect  than  that  of  Blaise 
Pascal  He  was  born  in  1623,  at  Clermont  in  Auvergne, 
and  from  his  earliest  years  displayed  signs  of  a  remark- 
able character.  His  father  attempted  at  first  to  prevent 
his  studying  geometry,  but  such  was  Pascal's  genius  and 
love  of  this  science,  that,  by  the  age  of  twelve,  he  had 
found  out  many  of  the  propositions  of  Euclid's  first  book 
without  the  aid  of  any  person  or  treatise.  It  is  difficult 
to  say  whether  he  is  most  to  be  admired  for  his  mathe- 
matical discoveries,  his  invention  of  the  first  calculating 
machine,  his  wonderful  Provincial  Letters  written  against 
the  Jesuits,  or  for  his  profound  Pense*es  or  Thoughts,  a 
collection  of  his  reflections  on  scientific  and  religious 
topics. 

Among  these  Thoughts  is  to  be  found  a  remarkable 
fragment  upon  Logical  method,  the  substance  of  which  is 
also  given  in  the  Port  Royal  Logic.  It  forms  the  second 
article  of  the  Pensees,  and  is  entitled  Reflexions  sur  la 
Geometric  en  general.  As  I  know  no  composition  in 
which  perfection  of  truth  and  clearness  of  expression  are 
more  nearly  attained,  I  propose  to  give  in  this  lesson  a 
free  translation  of  the  more  important  parts  of  this 


112  PASCAL  AND  DESCARTES         (.LESS 

fragment,  appending  to  it  rules  of  method  from  tht 
Port  Royal  Logic  and  from  Descartes'  celebrated  Essaj 
on  Method.  The  words  of  Pascal  are  nearly  as  follows. 

"The  true  method,  which  would  furnish  demonstrar 
tions  of  the  highest  excellence,  if  it  were  possible  tc 
employ  the  method  fully,  consists  in  observing  two  prin- 
cipal rules.  The  first  rule  is  not  to  employ  any  term  of 
which  we  have  not  clearly  explained  the  meaning;  the 
second  rule  is  never  to  put  forward  any  proposition  which 
we  cannot  demonstrate  by  truths  already  known ;  that  is 
to  say,  in  a  word,  to  define  all  the  terms,  and  to  prove  aH 
thf  propositions.  But,  in  order  that  I  may  observe  the 
rules  of  the  method  which  I  am  explaining,  it  is  neces- 
sary that  I  declare  what  is  to  be  understood  by  Definition, 

"We  recognise  in  Geometry  only  those  definitions 
which  logicians  call  Nominal  Definitions,  that  is  to  say, 
only  those  definitions  which  impose  a  name  upon  things 
clearly  designated  in  terms  perfectly  known ;  and  I  speak 
only  of  those  definitions." 

Their  value  and  use  is  to  clear  and  abbreviate  dis- 
course by  "expressing  in  the  single  name  which  we 
impose  what  could  not  be  otherwise  expressed  but  in 
several  words ;  provided  nevertheless  that  the  name  im- 
posed remain  divested  of  any  other  meaning  which  it 
might  possess,  so  as  to  bear  that  alone  for  which  we 
intend  it  to  stand. 

"For  example,  if  we  need  to  distinguish  among 
numbers  those  which  are  divisible  into  two  equal  parts, 
from  those  which  are  not  so  divisible,  in  order  to  avoid 
the  frequent  repetition  of  this  distinction,  we  give  a  name 
to  it  in  this  manner : — we  call  every  number  divisible  into 
two  equal  parts  an  Even  Number. 

"  This  is  a  geometrical  definition,  because  after  having 
clearly  designated  a  thing,  namely  any  numbei  divisible 
feto  two  equal  parts,  we  give  it  a  name  divesteU  of  every 


XIIL]  ON  METHOD.  113 

other  meaning,  which  it  might  have,  in  order  to  bestow 
upon  it  the  meaning  designated. 

"  Hence  it  appears  that  definitions  are  very  free,  and 
that  they  can  never  be  subject  to  contradiction,  for  there 
is  nothing  more  allowable,  than  to  give  any  name  we  wish 
to  a  thing  which  we  have  clearly  pointed  out.  It  is  only 
necessary  to  take  care  that  we  do  not  abuse  this  liberty  ol 
imposing  names,  by  giving  the  same  name  to  two  differ- 
ent things.  Even  that  would  be  allowable,  provided  that 
we  did  not  confuse  the  results,  and  extend  them  from 
one  to  the  other.  But  if  we  fall  into  this  vice,  we  have  a 
very  sure  and  infallible  remedy ; — it  is,  to  substitute  men- 
tally the  definition  in  place  of  the  thing  defined,  and  to 
hold  the  definition  always  so  present  in  the  mind,  that 
every  time  we  speak,  for  instance,  of  an  even  number,  we 
may  understand  precisely  that  it  is  a  number  divisible 
into  two  equal  parts,  and  so  that  these  two  things  should 
be  so  combined  and  inseparable  in  thought,  that  as  often 
as  one  is  expressed  in  discourse,  the  mind  may  direct  it- 
self immediately  to  the  other. 

"  For  geometers  and  all  who  proceed  methodically 
only  impose  names  upon  things  in  order  to  abbreviate 
discourse,  and  not  to  lessen  or  change  the  ideas  of  the 
things  concerning  which  they  discourse.  They  pretend 
that  the  mind  always  supplies  the  entire  definition  of  the 
biief  terms  which  they  employ  simply  to  avoid  the  con- 
fusion produced  by  a  multitude  of  words. 

"  Nothing  prevents  more  promptly  and  effectively  the 
insidious  fallacies  of  the  sophists  than  this  method,  which 
are  should  always  employ,  and  which  alone  suffices  to 
banish  all  sorts  of  difficulties  and  equivocations. 

"  These  things  being  well  understood,  J  return  to  my 
explanation  of  the  true  method,  which  consists,  as  I  said* 
in  defining  everything  and  proving  everything. 

"Certainly  this  method  would  be  an  excellent  one; 

8 


H4  PASCAL  AND  DESCARTES         [Lisa 

were  it  not  absolutely  impossible.  It  is  evident  that  th« 
nrst  terms  we  wished  to  define  would  require  previous 
terms  to  serve  for  their  explanation,  and  similarly  the 
first  propositions  we  wished  to  prove,  would  presuppose 
•  other  propositions  preceding  them  in  our  knowledge ;  and 
thus  it  is  clear  that  we  should  never  arrive  at  the  first 
terms  or  first  propositions. 

"Accordingly  in  pushing  our  researches  further  and 
further,  we  arrive  necessarily  at  primitive  words  which  we 
cannot  define,  and  at  principles  so  clear,  that  we  cannot 
find  any  principles  more  clear  to  prove  them  by.  Thus 
it  appears  that  men  are  naturally  and  inevitably  incapa- 
ble of  treating  any  science  whatever  in  a  perfect  method  $ 
but  it  does  not  thence  follow  that  we  ought  to  abandon 
every  kind  of  method The  most  perfect  method  avail- 
able to  men  consists  not  in  defining  everything  and  de- 
monstrating everything,  nor  in  defining  nothing  and  de- 
monstrating nothing,  but  in  pursuing  the  middle  course 
of  not  defining  things  which  are  clear  and  understood  by 
all  persons,  but  of  defining  all  others  ;  and  of  not  proving 
truths  known  to  all  persons,  but  of  proving  all  others. 
From  this  method  they  equally  err  who  undertake  to  de- 
fine and  prove  everything,  and  they  who  neglect  to  do  it 
in  things  which  are  not  self-evident." 

It  is  made  plain  in  this  admirable  passage  that  we 
can  never  by  using  words  avoid  an  ultimate  appeal  to 
things,  because  each  definition  of  a  word  must  require 
one  or  more  other  words,  which  also  will  require  defini- 
tion, and  so  on  ad  infinitum.  Nor  must  we  ever  rerun, 
back  upon  the  words  already  denned ;  for  if  we  define  A 
by  B,  and  B  by  C,  and  C  by  Z>,  and  then  D  by  A,  wt 
commit  what  may  be  called  a  circulus  in  definiettdo;  a 
most  serious  fallacy,  which  might  Jead  us  to  suppose  that 
we  know  the  nature  of  A,  B,  C,  and  D,  when  we  reall) 
nothing  about  them. 


XIII.]  ON  METHOD.  115 

Pascal's  views  of  the  geometrical  method  were  clearly 
rammed  up  in  the  following  rules,  inserted  by  him  in  the 
Port  Royal  Logic*. 

1.  To  admit  no  terms  in  the  least  obscure  or  equivo- 
cal urithout  defining  them. 

2.  To  employ  in  the  definitions  only  terms  perfectly 
known  or  already  explained. 

3.  To  demand  as  axioms  only  truths  perfectly  ev» 
dent. 

4.  To  prove  all  propositions  which  are  at  all  obscure, 
by  employing  in  their  proof  only  the  definitions  which 
have  preceded,  or  the  axioms  which  have  been  accorded, 
or  the  propositions  which  have  been  already  demonstrated, 
or  the  construction  of  the  thing  itself  which  is  in  dispute, 
when  there  may  be  any  operation  to  perform. 

5.  Never  to  abuse  the  equivocation  of  terms  by  failing 
to  substitute  for  them,  mentally,  the  definitions  which 
restrict  and  explain  them. 

The  reader  will  easily  see  that  these  rules  are  much 
more  easy  to  lay  down  than  to  observe,  since  even  geo- 
meters are  not  agreed  as  to  the  simplest  axioms  to  assume, 
or  the  best  definitions  to  make.  There  are  many  differ- 
ent opinions  as  to  the  true  definition  of  parallel  lines,  and 
the  simplest  assumptions  concerning  their  nature;  and 
how  much  greater  must  be  the  difficulty  of  observing 
Pascal's  rules  with  confidence  in  less  certain  branches  of 
science.  Next  after  Geometry,  Mechanics  is  perhaps  the 
most  perfect  science,  yet  the  best  authorities  have  been 
far  from  agreeing  as  to  the  exact  definitions  of  such 
notions  as  force ',  mass,  moment,  power,  inertia,  and  the 
most  different  opinions  are  still  held  as  to  the  simples! 
axioms  by  which  the  law  of  the  composition  of  forces  may 
be  proved  Nevertheless  if  we  steadily  bear  in  mind,  i» 

*  Mr  Spencei  Baynes'  Translation,  p.  317. 

8-* 


116  PASCAL  AND  DECARTES  [LESS 

studying  each  science,  the  necessity  of  defining  ev<ry  terra 
as  far  as  possible,  and  proving  each  proposition  which 
can  be  proved  by  a  simpler  one,  we  shall  do  much  to  cleat 
away  error  and  confusion. 

I  also  wish  to  give  here  the  rules  proposed  by  the 
celebrated  Descartes  for  guiding  the  reason  in  the  attain- 
ment of  truth.  They  are  as  follows  : — 

1.  Never  to  accept  anything  as  true,  which  we  dc 
not  clearly  know  to  be  so ;  that  is  to  say,  carefully  tc 
avoid  haste  or  prejudice,  and  to  comprise  nothing  more 
in  our  judgments  than  what  presents  itself  so  clearly  and 
distinctly  to  the  mind  that  we  cannot  have  any  room  to 
doubt  it 

2.  To  divide  each  difficulty  we  examine  into  as  mam 
parts  as  possible,    or  as  may  be  required  for    resolv- 
ing it. 

3.  To  conduct  our  thoughts  in  an  orderly  manner, 
commencing  with  the  most  simple  and  easily  known 
objects,  in  order  to  ascend  by  degrees  to  the  knowledge 
of  the  most  complex. 

4.  To  make  in  every  case  enumerations  so  complete, 
and  reviews  so  wide,  that  we  may  be  sure  of  omitting 
nothing. 

These  rules  were  first  stated  by  Descartes  in  his  ad- 
mirable Discourse  on  Method,  in  which  he  gives  his  reflec- 
tions on  the  right  mode  of  conducting  the  reason,  and 
searching  for  truth  in  any  of  the  sciences.  This  little 
treatise  is  easily  to  be  obtained  in  the  original  French,  and 
has  also  been  translated  into  English  by  Mr  Veitch*. 
The  reader  can  be  strongly  advised  to  study  it  Always  to 
observe  the  rules  of  Descartes  and  Pascal,  or  to  know 
vhether  we  in  every  case  observe  them  properly,  is  ua- 

•  Published  at  Edinburgh  in  1850. 


«ii.  j  ON  METHOD.  117 

possible,  but  it  must  nevertheless  be  valuable  to  know  as 
what  we  ought  to  aim. 

Read  Locke's  brief  Essay  on  the  Conduct  of  the  Un- 
derstanding^ which  contains  admirable  remarks  oc 
the  acquirement  of  exact  and  logical  habits  d 
thought 


m  xiv. 

THE  LAWS   OF  THOUGHT. 

BEFORE  the  reader  proceeds  to  the  lessons  which  treat 
of  the  most  common  forms  of  reasoning,  known  as  the 
syllogism,  it  is  desirable  that  he  should  give  a  careful 
attention  to  the  very  simple  laws  of  thought  on  which  all 
reasoning  must  ultimatel}  depend.  These  laws  describe 
the  very  simplest  truths,  in  which  all  people  must  agree, 
and  which  at  the  same  time  apply  to  all  notions  which 
we  can  conceive.  It  is  impossible  to  think  correctly  and 
avoid  evident  self-contradiction  unless  we  observe  what 
are  called  the  Three  Primary  Laws  of  fhovgnt,  which  may 
be  stated  as  follows . 

1.  The  Law  of  Identity.     Whatever  Is,  is. 

2.  The  Law  of  Contradiction    Nothing  can  both  be  and 

not  be. 
t.    The  Law  of  Excluded  Middle,    Brerythlnf  most 

either  be  or  not  be. 

Though  these  laws  when  thus  stated  may  seem  ab- 
lurdly  obvious,  and  were  ridiculed  by  Locke  and  others 
on  that  account,  I  have  found  that  students  are  seldom 
able  to  see  at  first  their  full  meaning  and  importance. 
ft  will  be  Dointed  out  in  Lesson  XXI 11.  that  logicians  haw 


lit  THE  LAWS  OF  THOUGHT.          J.L1S& 

overlooked  until  recent  years  the  very  simple  way  in  which 
all  arguments  may  be  explained  when  these  self-evident 
jaws  ai  e  granted ;  and  it  is  not  too  much  to  say  that  the 
whole  of  logic  will  be  plain  to  those  who  will  constantly 
use  these  laws  as  the  key. 

The  first  of  the  laws  may  be  regarded  as  the  best 
definition  we  can  give  of  identity  or  sameness.  Could 
any  one  be  ignorant  of  the  meaning  of  the  word  Identity, 
it  would  be  sufficient  to  inform  him  that  everything  IB 
Identical  with  itselt 

The  second  law  however  is  the  one  which  requires 
more  consideration.  Its  meaning  is  that  nothing  can 
have  at  the  same  time  and  at  the  same  place  contra- 
dictory and  inconsistent  qualities.  A  piece  of  paper  may 
be  blackened  in  one  part,  while  it  is  white  in  other  parts; 
or  it  may  be  white  at  one  time,  and  afterwards  become 
black;  but  we  cannot  conceive  that  it  should  be  both 
white  and  black  at  the  same  place  and  time.  A  door 
after  being  open  may  be  shut,  but  it  cannot  at  once  be 
shut  and  open.  Water  may  feel  warm  to  one  hand  and 
cold  to  another  hand,  but  it  cannot  be  both  warm  and 
cold  to  the  same  hand.  No  quality  can  both  be  present 
and  absent  at  the  same  time ;  and  this  seems  to  be  the 
most  simple  and  general  truth  which  we  can  assert  of  all 
things.  It  is  the  very  nature  of  existence  that  a  thing 
cannot  be  otherwise  than  it  is ;  and  it  may  be  safely  said 
that  all  fallacy  and  error  arise  from  unwittingly  reason- 
ing in  a  way  inconsistent  with  this  law.  All  statements 
or  inferences  which  imply  a  combination  of  contradictory 
qualities  must  be  taken  as  impossible  and  false,  and  the 
breaking  of  this  law  is  the  mark  of  their  being  false.  It 
can  easily  be  shewn  that  if  Iron  be  a  metal,  and  every 
metal  an  element,  Iron  must  be  an  element  or  it  can  be 
nothing  at  all,  since  it  would  combine  qualities  which  an 
inconsistent  (see  Lesson  xxin). 


MV.J  THE  LAWS  OF  THOUGHT.  11$ 

rhe  Law  of  Excluded  Middle  is  much  less  self-evidem 
than  either  of  the  two  preceding  ones,  and  the  reader  will 
not  perhaps  see  at  the  first  moment  that  it  is  equally 
important  and  necessary  with  them.  Its  meaning  may 
be  best  explained  by  saying  that  it  is  impossible  to  men- 
tion any  thing  and  any  quality  or  circumstance,  without 
allowing  that  the  quality  or  circumstance  either  belongs 
to  the  thing  or  does  not  belong.  The  name  of  the  law 
expresses  the  fact  that  there  is  no  third  or  middle  course ; 
the  answei  must  be  Yes  or  No.  Let  the  thing  be  rock 
and  the  quality  hard;  then  rock  must  be  either  hard  or 
not-hard.  Gold  must  be  either  white  or  not  white;  a 
line  must  be  either  straight  or  not  straight ;  an  action 
must  be  either  virtuous  or  not  virtuous.  Indeed  when 
we  know  nothing  of  the  terms  used  we  may  never- 
theless make  assertions  concerning  them  in  accordance 
with  this  law.  The  reader  may  not  know  and  in  fact 
chemists  may  not  really  know  with  certainty,  whether 
vanadium  is  a  metal  or  not  a  metal,  but  any  one  knows 
that  it  must  be  one  or  the  other.  Some  readers  may  not 
know  what  a  cycloid  is  or  what  an  isochronous  curve  is ; 
but  they  must  know  that  a  cycloid  is  either  an  isochro- 
nous curve  or  it  is  not  an  isochronous  curve. 

This  law  of  excluded  middle  is  not  so  evident  but  that 
plausible  objections  may  be  suggested  to  it.  Rock,  it 
may  be  urged,  is  not  always  either  hard  or  soft,  for  it  may 
be  half  way  between,  a  little  hard  and  a  little  soft  at  the 
same  time.  This  objection  points  to  a  distinction  which 
is  of  great  logical  importance,  and  when  neglected  often 
leads  to  fallacy.  The  law  of  excluded  middle  affirmed 
nothing  about  hard  and  soft,  but  only  referred  to  hard 
and  not-kard;  if  the  reader  chooses  to  substitute  soft  for 
not-hard  he  falls  into  a  serious  confusion  between  opposite 
terms  and  contradictory  terms.  It  is  quite  possible  that 
ft  thing  may  be  neither  hard  nor  soft,  being  half  way 


120  THE  LAWS  OF  THOUGHT.         [LESS 

between ;  but  in  that  case  it  cannot  be  fairly  called  hard 
so  that  the  law  holds  true.  Similarly  water  must  be 
either  warm  or  not-warm,  but  it  does  not  follow  that  it 
must  be  warm  or  cold.  The  alternative  not-warm  evi- 
dently includes  all  cases  in  which  it  is  cold  besides  cases 
where  it  is  of  a  medium  temperature,  so  that  we  should 
^all  it  neither  warm  nor  cold.  We  must  thus  carefully 
distinguish  questions  of  degree  or  quantity  from  those  of 
simple  logical  fact.  In  cases  where  a  thing  or  quality 
may  exist  to  a  greater  or  less  extent  there  are  many  alter- 
natives. Warm  water,  for,  instance  may  have  any  tempe- 
rature from  70°  perhaps  up  to  120°.  Exactly  the  same 
question  occurs  »u  cases  uf  geometrical  reasoning;  for 
Euclid  in  his  Elements  frequently  argues  from  the  self- 
evident  truth  that  any  line  must  be  either  greater  than, 
equal  to,  or  less  than  any  other  line.  While  there  are 
only  two  alternatives  to  choose-  from  in  logic  there  are 
three  in  Mathematics;  thus  one  line,  compared  with 
another,  may  be — 

jgreater greater  i  ^ 

In  Ix*ic.  (..ot^eater...)  ••••-.«£*    JMathemadcs. 

Another  and  even  more  plausible  objection  may  be 
raised  to  the  third  la«r  of  thought  in  this  way.  Virtue 
being  the  thing  proposed,  and  triangular  the  quality,  the 
Law  of  Excluded  Middle  enables  us  at  once  to  assert  that 
rirtue  is  either  triangular  or  not-triangular.  At  tirst  sight 
it  might  seem  false  and  absurd  to  say  that  an  immaterial 
notion  such  as  virtue  should  be  either  triangular  or  not, 
because  it  has  nothing  in  common  with  those  material 
substances  occupying  space  to  which  the  notion  of  figure 
belongs.  But  the  absurdity  would  arise,  not  from  any 
falseness  in  the  law,  but  from  misinterpretation  of  the 
expression  not-triangular.  If  in  saying  that  a  thing  if 


WV.J  THE  LAWS  OF  THOUGHT.  121 

"not  triangular"  we  are  taken  to  imply  that  it  has  some 
figure  though  not  a  triangular  figure,  then  of  course  the 
expression  cannot  be  applied  to  virtue  or  anything  im* 
material.  In  strict  logic  however  no  such  implied  mean* 
ing  is  to  be  allowed,  and  not-triangular  will  include  both 
things  which  have  figure  other  than  triangular,  as  well  as 
things  which  have  not  the  properties  of  figure  at  all;  and 
it  is  in  the  latter  meaning  that  it  is  applicable  to  an  im- 
material thing. 

These  three  laws  then  being  universally  and  neces- 
sarily true  to  whatever  things  they  are  applied,  become 
the  foundation  of  reasoning.  All  acts  of  reasoning  pro- 
ceed from  certain  judgments,  and  the  act  of  judgment 
consists  in  comparing  two  things  or  ideas  together  and 
discovering  whether  they  agree  or  differ,  that  is  to  say 
whether  they  are  identical  in  any  qualities.  The  laws  of 
thought  inform  us  of  the  very  nature  of  this  identity  with 
which  all  thought  is  concerned.  But  in  the  operation 
of  discourse  or  reasoning  we  need  certain  additional 
laws,  or  axioms,  or  self-evident  truths,  which  may  be  thus 
stated  : 

1.  Two  terms  agreeing  with  one  and  the  same  third 
term  agree  with  each  other. 

2.  Two  terms  of  which  one  agrees  and  the  other  dots 
not  agree  with  one  and  the  same  third  term,  do  not  agru 
with  each  other. 

These  self-evident  truths  are  commonly  called  the 
Canons  or  Fundamental  Principles  of  Syllogism,  and  they 
are  true  whatever  may  be  the  kind  of  agreement  in  ques- 
tion. The  example  we  formerly  used  (p.  3)  of  the  a 
greement  of  the  terms  "Most  useful  metal"  and  "cheapest 
snetal"  with  the  third  common  term  "  Iron,"  was  but 
in  instance  of  the  first  Canon,  and  the  agreement  con- 
iisted  in  complete  identity.  In  the  case  of  the  "  Earth," 
the  "  Planets,"  and  "  Bodies  revolving  in  elliptic  orbits,' 


122  THE  LAWS  OF  THOUGHT.         [LESS 

the  agreement  was  less  complete,  because  the  Earth  h 
only  one  of  many  Planets,  and  the  Planets  only  a  smafi 
portion  of  all  the  heavenly  bodies,  such  as  Satellites, 
Comets,  Meteors,  and  Double-Stars  which  revolve  in 
such  orbits. 

The  second  of  the  Canons  applies  to  cases  where  there 
fe  disagreement  or  difference,  as  in  the  following  example  : 
Venus  is  a  planet 
Planets  are  not  self-luminous. 
Therefore  Venus  is  not  self-luminous. 
The  first  of  these  propositions  states  a  certain  agree- 
ment to  exist  between  Venus  and  planet,  just  as  in  the 
previous  case  of  the  Earth,  but  the  second  proposiiion 
states  a  disagreement  between  Planet  and  self-luminous 
bodies;  hence  we  infer  a  disagreement  between  Venus 
and   self-luminous  body.     But  the  reader  will  carefully 
observe  that  from  two  disagreements  we  can  never  infer 
anything.     If  the  following  were  put  forth  as  an  argu- 
ment it  would  be  evidently  absurd : — 
Sirius  is  not  a  planet. 
Planets  are  not  self-luminous. 
Therefore  Sirius  is  not  self-luminous. 

Both  the  premises  or  propositions  given  are  true, 
and  yet  the  conclusion  is  false,  for  all  the  fixed  stars  are 
self-luminous,  or  shine  by  their  own  light.  We  may,  in 
fact,  state  as  a  third  Canon  that — 

3.  Two  terms  both  disagreeing  with  one  and  tht 
same  third  term  may  or  may  not  agree  with  each  other. 

Self-evident  rules,  of  an  exactly  similar  nature  to  these 
three  Canons,  are  the  basis  of  all  mathematical  reasoning, 
and  are  usually  called  axioms.  Euclid's  first  axiom  it 
that  "Things  which  are  equal  to  the  same  thing  are  equal 
to  one  another ;"  and  whether  we  apply  it  to  the  length  of 
tines,  the  magnitude  of  angles,  areas,  solids,  numbers. 


xiv.]  THE  LAWS  OF  THOUGHT.  ut 

degrees,  or  anything  else  which  admits  of  being  equal  of 
unequal,  it  holds  true.  Thus  if  the  lines  A  and  B  are  each 
equal  to  C  it  is  evident  that  each  is  equal  to  the  < 


A 

B  • 
C  - 
D  • 
E  • 


Euclid  does  not  give  axioms  corresponding  to  the  second 
and  third  Canons,  but  they  are  really  used  in  Geometry, 
Thus  if  A  is  equal  to  B,  but  D  is  not  equal  to  B,  it  follows 
that  A  is  not  equal  to  Z>,  or  things  of  which  one  is  equal, 
but  the  other  unequal  to  the  same  third  thing,  are  unequal 
to  each  other.  Lastly,  A  and  E  are  two  lines  both  un- 
equal to  D  and  unequal  to  each  other,  whereas  A  and  B 
are  two  lines  both  unequal  to  D  but  equal  to  each  other; 
thus  we  plainly  see  that  "  two  things  both  unequal  to  the 
same  thing  may  or  may  not  be  equal  to  each  other." 

From  what  precedes  it  will  be  apparent  that  all  rea 
soning  requires  that  there  should  be  one  agreement  at 
least;  if  there  be  two  agreements  we  may  reason  to  a 
third  agreement;  if  there  be  one  agreement  and  one 
difference  we  may  reason  to  a  second  difference ;  but  if 
there  be  two  differences  only  we  cannot  reason  to  any 
conclusion  whatever.  These  self-evident  principles  will 
in  the  next  Lesson  serve  to  explain  some  of  the  rules  of 
the  Syllogism. 

Logicians  however  have  not  confined  themselves  to 
the  use  of  these  Canons,  but  have  often  put  the  same 
truth  into  a  different  form  in  axioms  known  as  the  Dicta 
dt  omni  et  nullo  of  Aristotle.  This  celebrated  Latin 
phrase  means  "  Statements  concerning  all  and  none,"  and 
the  axiom,  or  rather  pair  of  axioms,  is  usually  given  iv 
the  following  words : 


124  THE  LAWS  OP    THOUGHT.         [LESJ 

Whatever  is  predicated  of  a  term  distributed  whether 
affirmatively  or  negatively,   may   be  predicated  in  Itiu 
manner  of  everything  contained  under  it. 
Or  more  briefly : 

What  pertains  to  the  highet  class  pertains  als*  to  tJu 
lower. 

This  merely  means,  in  untechnical  language,  that 
what  may  be  said  of  all  the  things  of  any  sort  or  kind 
may  be  said  of  any  one  or  any  cart  of  those  things ;  and, 
secondly,  what  may  be  denied  of  all  the  things  in  a  class 
may  be  denied  of  any  one  or  any  part  of  them.  What- 
ever may  be  said  of  "  All  planets  "  may  be  said  of  Venus, 
the  Earth,  Jupiter,  or  any  other  planet ;  and,  as  they  may 
all  be  said  to  revolve  in  elliptic  orbits,  it  follows  that 
this  may  be  asserted  of  Venus,  the  Earth,  Jupiter,  or  any 
other  planet  Similarly,  accoruing  to  the  negative  part 
of  the  Dicta,  we  may  deny  that  the  planets  are  self- 
luminous,  and  knowing  that  Jupiter  is  a  planet  may  deny 
that  Jupiter  is  self-luminous.  A  little  reflection  would 
show  that  the  affirmative  Dictum  is  really  the  first  of  the 
Canons  in  a  less  complete  and  general  form,  and  that  the 
negative  Dictum  is  similarly  the  second  Canon.  These 
Dicta  in  fact  only  apply  to  such  cases  of  agreement  be- 
tween terms  as  consist  in  one  being  the  name  of  a  smaller 
class,  and  another  of  the  larger  class  containing  it  Lo- 
gicians have  for  the  most  part  strangely  overlooked  the 
important  cases  in  which  one  term  agrees  with  another  to 
the  extent  of  being  identical  with  it ;  but  this  is  a  subject 
which  we  cannot  fitly  discuss  here  at  any  length.  It  is 
treated  in  my  little  work  called  The  Substitution  oj 
Similars*. 

Some  logicians  have  held  that  in  addition  to  the  three 
tews  which  are  called  the  Primary  Laws  of  Thought, 

*  Macmilkn  and  Co.  1869. 


XIV.]  THE  LAWS  OF  THOUGHT.  ia* 

there  is  a  fourth  called  "  The  Principle  or  Law  of  Sum 
cient  Reason."  It  was  stated  by  Leibnitz  in  the  following 
words  : 

Nothing  happens  without  a  reason  why  it  should  bi 
96  rather  than  otherwise.  For  instance,  if  there  be  a  pail 
tf  scales  in  every  respect  exactly  alike  on  each  side  and 
arith  exactly  equal  weights  in  each  scale,  it  must  remain 
motionless  and  in  equilibrium,  because  there  is  no  reason 
why  one  side  should  go  down  more  than  the  other.  It  is 
certainly  a  fundamental  assumption  in  mechanical  science 
that  if  a  body  is  acted  upon  by  two  perfectly  equal  forces 
m  different  directions  it  will  move  equally  between  them, 
because  there  is  no  reason  why  it  should  move  more  to 
one  side  than  the  other.  Mr  Mansel,  Sir  W.  Hamilton 
and  others  consider  however  that  this  law  has  no  place 
in  logic,  even  if  it  can  be  held  self-evident  at  all ;  and  the 
question  which  appears  open  to  doubt  need  not  be  dis- 
cussed here. 

I  have  so  freely  used  the  word  axiom  in  this  lesson 
that  it  is  desirable  to  clear  up  its  meaning  as  far  as  pos- 
sible. Philosophers  do  not  perfectly  agree  about  its  deri- 
vation or  exact  meaning,  but  it  certainly  comes  from  the 
verb  d£io'«,  which  is  rendered,  to  think  worthy.  It  gene- 
rally denotes  a  self-evident  truth  of  so  simple  a  character 
that  it  must  be  assumed  to  be  true,  and,  as  it  cannot  be 
proved  by  any  simpler  proposition,  must  itself  be  taken  aa 
the  basis  of  reasoning.  In  mathematics  it  is  clearly  used 
'•n  this  sense. 

See  Hamilton's  Lectures  on,  Logic,  Lectures  5  and  & 


^  LESSON   XV 

THE  RULES  OF  THE  SYLLOGISM. 

SYLLOGISM  is  the  common  name  for  Mediate  Inference, 
or  inference  by  a  medium  or  middle  term,  and  is  to  Ix 
distinguished  from  the  process  of  Immediate  Inference,  01 
inference  which  is  performed  without  the  use  of  any  third 
or  middle  term. 

We  are  in  the  habit  of  employing  a  middle  term  or 
medium  whenever  we  are  prevented  from  comparing  two 
things  together  directly,  but  can  compare  each  of  them 
with  a  certain  third  thing.  We  cannot  compare  the  sizes 
of  two  halls  by  placing  one  in  the  other,  but  we  can 
measure  each  by  a  foot  rule  or  other  suitable  measure, 
which  forms  a  common  measure,  and  enables  us  to  ascei 
tain  with  any  necessary  degree  of  accuracy  their  relative 
dimensions.  If  we  have  two  quantities  of  cotton  goods 
and  want  to  compare  them,  it  is  not  necessary  to  bring 
fhe  whole  of  one  portion  to  the  other,  but  a  sample  is  cut 
off,  which  represents  exactly  the  quality  of  one  portion, 
and,  according  as  this  sample  does  or  does  not  agree  with 
the  other  portion,  so  must  the  two  portions  of  goods  agree 
or  differ. 

The  use  of  a  middle  term  in  syllogism  is  closely  pa- 
rallei  to  what  it  is  in  the  above  instances,  but  not  exactly 
the  same.  Suppose,  as  an  example,  that  we  wish  to 
ascertain  whether  or  not  "Whales  are  viviparous,"  and 
mat  we  had  not  an  opportunity  of  observing  the  fact 
directly ;  we  could  yet  show  it  to  be  so  if  we  knew  that 
**  whales  are  mammalian  animals,"  and  that  "  ^11  ; 


XV.]     THE  RULES  OF  THE  SYLLOGISM.       i*t 

malian  animals  are  viviparous."  It  would  follow  tha». 
"  whales  are  viviparous ; "  and  so  far  as  the  inference  if 
concerned  it  does  not  matter  what  is  the  meaning  wt 
attribute  to  the  words  viviparous  and  mammalian.  la 
this  case  "  mammalian  animal "  is  the  middle  term, 

The  name  Syllogism  means  the  joining  together  ia 
Jiought  of  two  propositions,  and  is  derived  from  the 
Greek  words  <n5i/,  with,  and  Xoyor,  thought  or  reason.  It 
is  thus  exactly  the  equivalent  of  the  word  Computation, 
which  means  thinking  together  (Latin  cont  together, 
$uto,  to  think),  or  reckoning.  In  a  syllogism  we  so  unite 
in  thought  two  premises,  or  propositions  put  forward,  that 
we  are  enabled  to  draw  from  them  or  infer,  by  means  of 
the  middle  term  they  contain,  a  third  proposition  called 
the  conclusion.  Syllogism  may  thus  be  defined  as  the 
act  of  thought  by  which  from  two  given  propositions  we 
proceed  to  a  third  proposition,  the  truth  of  which  neces- 
sarily follows  from  the  truth  of  these  given  propositions. 
When  the  argument  is  fully  expressed  in  language  it  is 
usual  to  call  it  concretely  a  syllogism. 

The  special  rules  of  the  syllogism  are  founded  upon 
the  Laws  of  Thought  and  the  Canons  considered  in  the 
previous  Lesson.  They  serve  to  inform  us  exactly  under 
what  circumstances  one  proposition  can  be  inferred  from 
two  other  propositions,  and  are  eight  in  number,  as 
follows  : — 

I.     Every  syllogism  has  three  and  only  three  terms. 

These  terms  are  called  the  major  term,  the  minoi 
term,  and  the  middle  term, 

3>  Every  syllogism  contains  three,  at<d  only  thru 
propositions. 

These  propositions  are  called  the  major  premise,  th« 
minor  premise,  and  the  conclusion. 

3.  The  middle  term  must  be  distributed  once  at  Uast, 
and  must  not  be  ambiguous. 


128       THE  RULES  OF  THE  SYLLOGISM.  [LES& 

4.  No  term  must  be  distributed  in  the  conclusion 
which  was  not  distributed  in  one  of  the  premises. 

5.  From  negative  premises  nothing  can  be  inferred. 

6.  If  one  premise  be  negative,  the  conclusion  must 
be  negative;   and  vice  versa,  to  prove  a  negative  con* 
elusion  one  of  the  premises  must  be  negative. 

From  the  above  rules  may  be  deduced  two  subor- 
dinate rules,  which  it  will  nevertheless  be  convenient  to 
state  at  once. 

7.  From  two  particular  premises  no  conclusion  can 
b*  drawn. 

8.  If  one  premise  be  particular jtht  conclusion  mutt 
be  particulaA 

All  these  rules  are  of  such  extreme  importance  that  it 
will  be  desirable  for  the  student  not  only  to  acquire  a 
perfect  comprehension  of  their  meaning  and  truth,  but  to 
commit  them  to  memory.  During  the  remainder  of  this 
lesson  we  shall  consider  their  meaning  and  force. 

As  the  syllogism  consists  in  comparing  two  terms  by 
means  of  a  middle  term,  there  cannot  of  course  be  less 
than  three  terms,  nor  can  there  be  more  ;  for  if  there 
were  four  terms,  say  A,  B,  C,  Z>,  and  we  compared  A 
with  B  and  C  with  Z>,  we  should  either  have  no  common 
medium  at  all  between  A  and  Z?,  or  we  should  require  a 
second  syllogism,  so  as  first  to  compare  A  and  C  with  Bt 
and  then  A  and  D  with  C. 

The  middle  term  may  always  be  known  by  the  fact 
ihat  it  does  not  occur  in  the  conclusion.  The  major  term 
is  always  the  predicate  of  the  conclusion,  and  the  minor 
Una  the  subject.  These  terms  are  thus  called  because  in 
the  universal  affirmative  proposition  (,A)  the  predicate  is 
necessarily  a  wider  or  greater  or  major  term  than  the 
subject ;  thus  in  "  all  men  are  mortals,"  the  predicate  in- 
cludes all  other  animals  as  well  as  men,  and  i*  obviously 
a  major  term  or  wider  term  than  men. 


XV.]     THE  RULES  OF  THh  SYLLOGISM.       129 

Again,  the  syllogism  necessarily  consists  of  a  premise 
called  the  major  premise,  in  which  the  major  and  middle 
terms  are  compared  together;  of  a  minor  premise  which 
similarly  compares  the  minor  and  middle  terms ;  and  of 
a  conclusion,  which  contains  the  major  and  minor  terms 
jnly.  In  a  strictly  correct  syllogism  the  major  premise 
ilways  stands  before  the  minor  premise,  but  in  ordinary 
writing  and  speaking  this  rule  is  seldom  observed ;  and 
that  premise  which  contains  the  major  term  still  con- 
tinues to  be  the  major  premise,  whatever  may  be  its 
position. 

The  third  rule  is  a  very  important  one,  because  many 
fallacies  arise  from  its  neglect.  By  the  middle  term  being 
distributed  once  at  least,  we  mean  (see  p.  74)  that  the 
whole  of  it  must  be  referred  to  universally  in  one  premise, 
if  not  both.  The  two  propositions — 

All  Frenchmen  are  Europeans, 
All  Russians  are  Europeans, 

do  not  distribute  the  middle  term  ar  all,  because  Uiey 
are  both  affirmative  propositions,  which  have  (p.  75) 
undistributed  predicates.  It  is  apparent  that  French- 
men are  one  part  of  Europeans,  and  Russians  anothei 
part,  as  shown  in  Killer's  method  In  Fig.  6,  so  thai 


Ijo    THE  RULES  OF  THE  SYLLOGISM.    [LE*S 

there  is  no  real  middle  term.  Those  propositions  would 
equally  allow  of  Russians  being  or  not  being  Frenchmen  j 
for  whether  the  two  interior  circles  overlap  or  not  they 
are  equally  within  the  larger  circle  of  Europeans  Again 
the  two  propositions 

All  Frenchmen  are  Europeans, 

All  Parisians  are  Europeans, 

10  not  enable  us  to  infer  that  all  Parisians  are  French 
men.  For  though  we  know  of  course  that  all  Parisians 

Fig.  7- 


are  included  among  Frenchmen,  the  premises  would 
allow  of  their  being  placed  anywhere  within  the  circle  ol 
Europeans.  We  see  in  this  instance  that  the  premises 
and  conclusion  of  an  apparent  argument  may  all  be  true 
and  yet  the  argument  may  be  fallacious. 

The  part  of  the  third  rule  which  refers  to  an  ambi 
guoms  middle  term  hardly  requires  explanation.  It  has 
been  stated  (Lesson  iv.)  that  an  ambiguous  term  is  one 
which  has  two  different  meanings,  implying  different  con 
notations,  and  it  is  really  equivalent  to  two  different  terms 
which  happen  to  have  the  same  form  of  spelling,  so  that 
they  are  readily  mistaken  for  each  other.  Thus  if  we 
were  to  argue  that  because  **  all  metals  are  elements  and 


XV.]     THE  RULES  OF  THE  SYLLOGISM.      I) 

brass  is  metal,  therefore  it  is  an  element,"  we  should  bt 
committing  a  fallacy  by  using  the  middle  term  metal  it 
two  different  senses,  in  one  of  which  it  means*  the  pure 
simple  substances  known  to  chemists  as  metals,  and  in 
the  other  a  mixture  of  metals  commonly  called  metal  in 
the  arts,  but  known  to  chemists  by  the  name  alloy.  In 
many  examples  which  may  be  found  in  logical  books  the 
ambiguity  of  the  middle  term  is  exceedingly  obvious,  but 
the  reader  should  always  be  prepared  to  meet  with  cases 
where  exceedingly  subtle  and  difficult  cases  of  ambiguity 
occur.  Thus  it  might  be  argued  that  "what  is  right 
should  be  enforced  by  law,  and  that  charity  is  right  and 
should  therefore  be  enforced  by  the  law."  Here  it  is 
evident  that  right  is  applied  in  one  case  to  what  the 
conscience  approves,  and  in  another  case  to  what  public 
opinion  holds  to  be  necessary  for  the  good  of  society. 

The  fourth  rule  forbids  us  to  distribute  a  term  in  the 
conclusion  unless  it  was  distributed  in  the  premises.  As 
the  sole  object  of  the  syllogism  is  to  prove  the  conclusion 
by  the  premises,  it  is  obvious  that  we  must  not  make  a 
statement  concerning  anything  unless  that  thing  was 
mentioned  in  the  premises,  in  a  way  warranting  the  state- 
ment. Thus  if  we  were  to  argue  that  "  because  many 
nations  are  capable  of  self-government  and  that  nations 
capable  of  self-government  should  not  receive  laws  from  a 
despotic  government,  therefore  no  nation  should  receive 
laws  from  a  despotic  government,"  we  should  be  clearly 
exceeding  the  contents  of  our  premises.  The  minor  term, 
many  nations,  was  particular  in  the  minor  premise,  and 
aiust  not  be  made  universal  in  the  conclusion.  The  pre- 
mises do  not  warrant  a  statement  concerning  anything  but 
the  many  nations  capable  of  self-government.  The  above 
argument  would  therefore  be  fallacious  and  would  b$ 
technically  called  an  Ulicit  process  of  the  minor  term, 
meaning  that  we  have  improperly  treated  the  minor  term 

o— a 


133      THE  RULES  OF  THE  SYLLOGISM.  [LESi 

Such  a  breach  of  the  fourth  rule  as  is  described  above 
is  exceedingly  easy  to  detect,  and  is  therefore  very  seldom 
committed. 

But  an  Ulldt  process  or  improper  treatment  of  the 
major  term  is  more  common  because  it  is  not  so  trans- 
parently fake.  If  we  argued  indeed  that  "because  all 
Anglo-Saxons  love  liberty,  and  Frenchmen  are  not  Anglo- 
Saxons,  therefore  they  do  not  love  liberty,"  the  fallacy 
would  be  pretty  apparent;  but  without  a  knowledge  of 
logic  it  would  not  be  easy  to  give  a  clear  explanation  of 
the  fallacy.  It  is  apparent  that  the  major  term  loving 
liberty,  is  undistributed  in  the  major  premise,  so  that 
Anglo-Saxons  must  be  assumed  to  be  only  a  part  of  those 
who  love  liberty.  Hence  the  exclusion  of  Frenchmen 
from  the  class  Anglo-Saxons  does  not  necessarily  exclude 
them  from  the  class  who  love  liberty  (see  Fig.  8).  The 

Fig.  8. 


conclusion  of  the  false  argument  being  negative  distri- 
butes its  predicate,  the  major  term,  and  as  this  is  un- 
distributed in  the  major  premise  we  have  an  Illicit  majox 
as  we  may  briefly  call  this  fallacy.  The  following  is  an 
obscurer  example  of  the  same  fallacy ; — "  Few  students 


t?.]     THE  RULES  OF  THE  SYLLOGISM.       133 

are  capable  of  excelling  in  many  branches  of  knowledge, 
ind  such  as  can  so  excel  are  deserving  of  high  commen- 
dation ;"  hence  "  few  students  are  deserving  of  high  com* 
mendation."  The  little  word  "  few  "  has  here  the  doubit 
meaning  before  explained  (p.  67),  and  means  that  "a 
few  are,  &c.,  and  the  rest  are  not"  The  conclusion  is 
thus  really  a  negative  proposition,  and  distributes  the 
major  term  "deserving  of  high  commendation."  But 
this  major  term  is  clearly  undistributed  in  the  major 
premise,  which  merely  asserts  that  those  who  can  excel 
in  many  branches  of  knowledge  are  deserving,  but  says 
or  implies  nothing  about  other  students. 

The  fifth  rule  is  evidently  founded  on  the  principle 
noticed  in  the  last  lesson,  that  inference  can  only  proceed 
where  there  is  agreement,  and  that  two  differences  or 
disagreements  allow  of  no  reasoning.  Two  terms,  as  the 
third  Canon  states,  may  both  differ  from  a  common  term 
and  yet  may  or  may  not  differ  from  each  other.  Thus  il 

Fig.  9. 


LEunptaauA 


we  were  to  argue  that  Americans  are  not  Europeans,  and 
Virginians  are  not  Europeans,  we  see  that  both  termi 
iisagree  with  the  middle  term  Europeans,  and  yet  they 


134     THE  RULES  OF  THE  SYLLOGISM     ^LESB 

agree  between  themselves.  In  other  cases  the  two  nega- 
tire  premises  may  be  plainly  true  while  it  ^  ill  be  quite 
uncertain  whether  the  major  and  minor  terms  agree  or 
not  Thus  it  is  true,  for  ««t»««^  that  "Colonists  are 
not  Europeans,  and  Americans  are  not  Europeans,"  but 
this  gives  us  no  right  to  infer  that  Colonists  are  at 
are  not  Americans.  The  two  negative  premises  are  re- 
presented in  fig.  9,  by  excluding  the  circles  of  Colonists 
and  Americans  from  that  of  Europeans ;  but  this  exclusion 
may  still  be  effected  whether  Colonists  and  Americans 
coincide  partially,  or  wholly,  or  not  at  all  A  breach  oi 
this  rule  of  the  syllogism  may  be  conveniently  called  the 
fallacy  of  negative  premise*.  It  must  not  however  be 
supposed  that  the  mere  occurrence  of  a  negative  particle 
(not  or  no)  in  a  proposition  renders  it  negative  in  the 
manner  contemplated  by  this  rule.  Thus  the  argument 

"  What  is  not  compound  is  an  element 
Gold  is  not  compound  ; 
Therefore  Gold  is  an  element," 

contains  negatives  in  both  premises,  but  is  nevertheless 
^id,  because  the  negative  in  both  cases  affects  the  middle 
term,  which  is  really  the  negative  term  not-compound. 

The  truth  of  the  sixth  rule  depends  upon  that  of  the 
Mjuom,  that  if  two  terms  agree  with  a  common  third  term 
they  agree  with  each  other,  whence,  remembering  that  a 
negative  proposition  asserts  disagreement,  it  is  evident 
that  a  negative  conclusion  could  not  be  drawn  from  really 
affirmative  premises.  The  corresponding  negative  axiom 
prevents  our  drawing  an  affirmative  conclusion  if  either 
premise  should  be  really  negative.  Only  practice  how- 
ever  will  enable  the  student  to  apply  this  and  the 
preceding  rules  of  the  syllogism  with  certainty,  since 
fallacy  may  be  hidden  and  disguised  by  various  form$  of 
expression.  Numerous  examples  are  given  at  the  end  of 


**.]  THE  RULES  OF  THE  SYLLOGISM.         13 

I 

the  book  by  which   the  student  may  acquire  facility  in 
the  analysis  of  arguments. 

The  remaining  rules  of  the  syllogism,  the  ;th  and  8th, 
are  by  no  means  of  a  self-evident  character  and  are  in 
fact  corollaries  of  the  first  six  rules,  that  is  consequences 
*'hich  follow  from  them.  We  shall  therefore  have  to 
ihew  that  they  are  true  consequences  in  a  future  Lesson. 
We  may  call  a  breach  of  the  7th  rule  a  fallacy  of  parti- 
cular premises,  and  that  of  the  8th  rule  the  fallacy  of  a 
universal  conclusion  from  a  particular  premise^  but  these 
fallacies  may  really  be  resolved  into  those  of  Illicit 
Process,  or  Undistributed  Middle. 

Fcr  many  details  concerning  the  Aristotelian  and 
Scholastic  Views  of  the  Syllogism,  and  of  Formal 
Logic  generally,  see  the  copious  critical  notes  to 
Mans  el's  edition  of  Aldrich's  Art  is  Logic*  Rudi- 
nunta.  2nd  Ed.  Oxford.  1852. 


LESSON  XVI. 

THE  MOODS  AND   FIGURES  OF  THE 
SYLLOGISM. 

WE  are  now  in  full  possession  of  those  principles  of  rea- 
soning, and  the  rules  founded  upon  them,  by  which  a 
true  syllogism  may  be  known  from  one  which  only  seems 
to  be  a  true  one,  and  our  task  in  the  present  Lesson  is  to 
ascertain  the  various  shapes  or  fashions  in  which  a 
process  of  mediate  inference  or  syllogism  may  be  met 
with.  We  know  that  every  syllogistic  argument  must 
contain  three  propositions  and  three  distinct  terms  each 
occurring  twice  in  those  propositions.  Each  proposition 


!36  THE  MOODS  AND  FIGURES       [LKSti 

of  the  syllogism  may,  so  far  as  we  yet  know,  be  eitha 
affirmative  or  negative,  universal  or  particular,  so  that  it 
is  not  difficult  to  calculate  the  utmost  possible  varieties  of 
modes  in  which  a  syllogism  might  conceivably  be  con- 
structed. Any  one  of  the  four  propositions  A,  E,  I,  or  0  may 
in  short  be  taken  as  a  major  premise,  and  joined  with  any 
one  of  the  same  form  as  a  minor  premise,  and  any  one  ol 
^he  four  again  may  be  added  as  conclusion.  We  should 
thus  obtain  a  series  of  the  combinations  or  modes  of 
joining  the  letters  A,  E,  I,  0,  a  few  of  which  are  here  writ 
ten  out: 

AAA  AEA  AIA  AOA  EAA  EEA 
AAB  AEB  AIB  AOE  EAE  EEE 
AAI  AEI  All  AOI  EAI  EEI 
AAO  ABO  AIO  AOO  EAO  Ac. 

It  is  obvious  that  there  will  be  altogether  4x4x4  or  6/ 
such  combinations,  of  which  23  only  are  gfven  above 
The  student  can  easily  write  out  the  remainder  by  carry- 
ing on  the  same  systematic  changes  of  the  letters.  Thus 
beginning  with  AAA  we  change  the  right-hand  letter  suc- 
cessively into  E,  I,  and  0,  and  then  do  the  same  beginning 
with  AEA  instead ;  after  the  middle  letter  has  been  carried 
through  all  its  changes  we  begin  to  change  the  left-hand 
letter.  With  each  change  of  this  we  have  to  repeat  all 
the  sixteen  changes  of  the  other  letters,  so  that  there  will 
obviously  be  altogether  64  different  conceivable  modes 
/f  arranging  propositions  into  syllogisms. 

We  call  each  of  these  triplets  of  propositions  a  mood  or 
torrn  of  the  syllogism  (Latin  modus,  shape  ,  and  we  have 
o  consider  how  many  of  such  forms  can  really  be  used  in 
'alid  arguments,  as  distinguished  from  those  which  break 
«ie  or  more  of  the  rules  of  the  syllogism.  Thus  the  mood 
4EA  would  break  the  6th  rule,  that  if  one  premise  b« 
negative  the  conclusion  must  be  so  too;  AIE  breaks  the 


xvi.  J  OF  THE  SYLLOGISM.  137 

converse  part  of  the  same  rule,  that  a  negative  conclusion 
can  only  be  proved  by  a  negative  premise ;  while  ERA, 
EEE  &c.,  break  the  5th  rule,  which  prohibits  our  reasoning 
at  all  from  two  negative  premises.  Examples  of  any  oJ 
these  moods  can  easily  be  invented,  and  their  falsity  would 
be  very  apparent ;  thus  for  AEA  we  might  take 

All  Austrians  are  Europeans, 
No  Australians  are  Europeans ; 
Therefore,  all  Australians  are  Austrians. 

Many  of  the  64  conceivable  moods  are  excluded  by  the 
7th  and  8'th  rules  of  the  syllogism.  Thus  ATA  and  BH 
break  the  rule,  that  if  one  premise  be  particular  the  con- 
clusion must  be  so  also,  while  HA,  100,  010  and  many 
others,  break  the  rule  against  two  particular  premises. 
Some  combinations  of  propositions  may  break  more  than 
one  rule ;  thus  OOO  has  both  negative  premises  and  parti- 
cular premises,  and  OOA  also  violates  as  well  the  6th 
rule.  It  is  an  admirable  exercise  in  the  use  of  the  syl- 
logistic rides  to  write  out  all  the  64  combinations  and 
then  strike  out  such  as  break  any  ru4e ;  the  task  if  pur« 
sued  systematically  will  not  be  so  long  or  tedious  aj 
might  seem  likely.  It  will  be  found  that  there  are  only 
twelve  moods  which  escape  exclusion,  and  may  so  far  b« 
considered  good  forms  of  reasoning,  and  these  are 

AAA         EAE        IAI        010 

AAI         EAO       (ESO) 

AEB          EXO 

ABO 

AOO 

Of  these  however  IEO  will  have  shortly  to  oe  rejected, 
because  it  will  be  found  really  to  break  the  4th  rule,  and 
involves  Illicit  process  of  the  major  term.  There  arc 


138  THE  MOODS  AND  FIGURES       {LESS 

then,  only  eleven  moods  of  the  syllogism  which  are  reall) 
valid;  and  we  may  thus  account  for  the  whole  of  th« 
\ixty-four  moods. 

Numbex 
Excluded  by  of  mood* 

Negative  premises,  Rule   5 16 

Particular  premises      „     7 12 

One  negative  premise  „    6 12 

One  premise  particular,,    8 8 

Negative  conclusion     „    6 ~    4 

Illicit  major „   4. I 

Total  excluded 53 

Valid  moods II 

Total  64 

We  have  by  no  means  exhausted  as  yet  all  the 
possible  varieties  of  the  syllogism,  for  we  have  only  de- 
urmined  the  character,  affirmative  or  negative,  generai 
or  particular  of  the  propositions,  but  have  not  decided 
the  ways  in  which  the  terms  may  be  disposed  in  them. 
The  major  term  must  be  the  predicate  of  the  conclusion, 
but  it  may  either  be  subject  or  predicate  of  the  majoi 
premise,  and  similarly  the  minor  term  or  subject  of  the 
conclusion,  may  be  either  the  subject  or  predicate  of  the 
minor  premise.  There  thus  arise  four  different  ways,  01 
as  they  are  called  Figures,  in  which  the  terms  can  b€ 
disposed.  These  four  figures  of  the  syllogism  are  shewi 
in  the  following  scheme,  taking 

X  to  denote  the  major  term 

Y  middle  „ 

Z. minor   „ 

lit  Fig.  2nd  Fig.  3rd  Fig.  4th  Fig, 

Major  Premise    YX  XY  YX  XY 

Minor        „         ZY  ZY  YZ          YZ 

Conclusion          ZX  ZX  ZX  ZX 


XVI.]  OF  THE  SYLLOGISM.  139 

These  figures  must  be  carefully  committed  to  memory, 
which  will  best  be  done  by  noting  the  position  of  the 
middle  term.  This  term  stands  first  as  subject  of  the 
major  premise  in  the  ist  Figure,  second  as  predicate  ic 
both  premises  of  the  2nd  Figure,  first  again  as  subject  ol 
both  premises  in  the  3rd  Figure,  and  in  an  intermediate 
position  in  the  4th  Figure.  In  the  conclusion,  of  course, 
the  major  and  minor  terms  have  one  fixed  position,  and 
when  the  middle  term  is  once  correctly  placed  in  any 
figure  we  easily  complete  the  syllogism. 

The  reader  will  hardly  be  pleased  to  hear  that  each  of 
the  eleven  valid  moods  will  have  to  be  examined  in  each 
of  the  four  figures  separately,  so  that  there  are  44  cases 
still  possible,  from  which  the  valid  syllogisms  have  to  be 
selected.  Thus  the  mood  ABB  in  the  first  figure  would  be 
as  follows : 

All  K's  are  A?s, 
No  Z*s  are  K*s; 

Therefore  No  Z's  are  X*s. 

rhis  would  break  the  4th  rule  and  be  an  Illicit  Major, 
because  X  is  distributed  in  the  conclusion,  which  is  a 
negative  proposition,  and  not  in  the  major  premise.  In 
the  second  figure  it  would  be  valid: 

All  XJ*  are  KX 

NoZ'sare  K*s; 

Therefore  No  Z's  are  X1 1 

In  the  third  figure  it  becomes 

All  l"s  are  JT% 
No  K's  are  Z's, 
No  Z*s  are  A?$, 

and  again  breaks  the  4th  rule,  as  regards  the  major  term, 
Lastly  in  the  4th  figure  it  is  valid,  as  the  reader  may 
easily  satisfy  himself. 


140  TOT  MOODS  AND  FIGURES       £LES* 

When  all  the  valid  moods  are  selected  out  of  the  44 
possible  ones,  there  are  found  to  be  altogether  24,  whicb 
are  as  follows: 

Valid  Moods  of  th«  Syllogism. 

First     Second  Third  Fourth 

Figure.  Figure.  Figure.  Figure. 

AAA           BAE  AAI           AAI 

BAB           AEE  IAI           ABB 

All           BIO  All           1A1 

no     AGO     EAO     BAO 
OAO      BIO 

[BAO]         EIO 

[AEO]  [AEO] 

ive  of  the  above  moods  are  set  apart  and  enclosed  in 
brackets,  because  though  valid  they  are  of  little  or  no  use. 
They  are  said  to  have  a  weakened  conclusion,  because  the 
conclusion  is  particular  when  a  general  one  might  have 
been  drawn.  Thus  AAI,  in  the  first  figure  is  represented 
by  the  example : 

All  material  substances  gravitate, 
All  metals  are  material  substances ; 
Therefore  some  metals  gravitate. 

It  is  apparent  that  the  conclusion  only  states  a  part  of 
the  truth,  and  that  in  reality  a/I  metals  gravitate.  It  is 
not  actually  an  erroneous  conclusion,  because  it  must 
be  carefully  remembered  (p.  77  •  that  the  affirming  of  a 
subaltern  or  particular  proposition  does  not  deny  the 
corresponding  general  proposition.  It  is  quite  true  that 
tome  metals  gravitate,  and  it  must  be  true  because  all  of 
them  do  so.  Bat  when  we  can  as  readily  prove  that  ail 
4o  gravitate  it  is  desirable  to  ad«pt  this  conclusion. 

If  we  agree  with  most  logicians  to  overlook  the  ex- 
istence of  the  five  syllogisms  with  weakened  conclusions, 


XVI.]  OF  THE  SYLLOGISM.  141 

there  will  remain  nineteen  which  are  at  once  valid  and 
useful.  In  the  next  lesson  certain  ancient  mnemonic 
lines  will  be  furnished  by  which  alone  it  would  be  possible 
for  most  persons  to  carry  in  the  memory  these  19  combi 
nations ;  but  the  reader  will  in  the  mean  time  be  able  to 
gather  from  the  statement  of  the  moods  in  p.  140  the 
truth  of  the  following  remarks  concerning  the  peculiar 
character  of  each  figure  of  the  syllogism. 

The  first  figure  is  the  only  one  which  proves  the  pro- 
position A,  or  has  A  for  its  conclusion.  It  is  the  only 
figure,  too,  which  can  prove  any  one  of  the  four  proposi- 
tions A,  B,  I,  0.  As  regards  the  premises,  it  is  especially 
important  to  note  that  the  major  premise  is  always 
universal  (A  or  B),  and  the  minor  premise  affirmative  (A  01 
I) :  this  peculiarity  will  be  further  considered  in  the  next 
lesson. 

The  second  figure  only  proves  negative  conclusions 
(B  or  O),  and  the  reason  is  easily  apparent.  As  the  middle 
term  in  this  figure  is  the  predicate  of  both  premises  it 
would  necessarily  be  undistributed  in  both  premises  if 
these  were  affirmatives,  and  we  should  commit  the  fallacy 
exemplified  in  p.  137.  It  follows  that  one  premise  must 
be  negative  and  of  course  one  only,  so  that  of  the  major 
and  minor  terms  one  must  be  included  or  excluded  wholly 
from  the  middle,  and  the  other  at  the  same  time  excluded 
or  included  at  least  partially.  To  illustrate  this  we  may 
take  Xy  Y  and  Z  to  represent,  as  before,  the  major,  mid- 
lie  and  minor  terms  of  a  syllogism,  and  the  four  moodi  o< 
ihu  figure  are  then 

SAB  ABB 

noJTsare  Y>*>  aUJTsueFX 

ail  Z's  are  K*s  ;  no  Z's  are  K*§; 

/.  no  Z's  are  AT's.  .-.  no  Z's  are  X**, 


THE  MOODS  AND  FIGURES       [LESS 

AOO 

all  AT's  are  K% 
some  Z's  are  not  K*s  ; 
.  some  Z's  are  not  A';s. 


BIO 

no  AT's  arc  ^s, 
some  Z's  are  Vs  ; 
/.  iome  Z's  are  not  X 's. 


The  nature  of  the  moods  of  the  second  figure  is  clearl ' 
shewn  in  the  following  figures : 


Fig.  10. 

(Cesare.) 


Fig.  ii. 
(Camestret.) 


It  wfll  also  be  observed  that  in  the  second  figure  tk< 
aunor  premise  may  be  any  of  the  four  A,  B,  I,  0. 

The  third  figure  only  proves  particulars  (I  or  0  ,  and 
't  always  has  an  affirmative  minor  premise  (A  or  I).  II 
also  contains  the  greatest  number  of  moods,  since  in  nc 
case  is  the  conclusion  a  weakened  one. 


XTL]  OF  THE  SYLLOGISM.  143 

The  fourth  igure  is  usually  considered  unnatural  and 
comparatively  useless,  because  the  same  arguments  cat 
oe  more  clearly  arranged  in  the  form  of  the  first  figure, 
which  in  some  respects  it  resembles.  Thus  it  proves  all 
the  propositions  except  A,  namely,  E,  1,  0,  and  i*s  fir«« 
mood  AAI,  is  in  reality  a  weakened  form  of  AAA  in  the 
first  figure.  Many  logicians,  including  in  recent  times 
Sir  W.  Hamilton,  have  rejected  the  use  of  this  figure 
altogether. 

It  is  evident  that  the  several  figures  of  the  syllogism 
possess  different  characters,  and  logicians  have  thought 
that  ea<h  figure  was  best  suited  for  certain  special  pur- 
pose*. A  German  logician,  Lambert,  stated  these  pur- 
pose concisely  as  follows  :— *'  The  first  figure  is  suited  to 
the  discovery  or  proof  of  the  properties  of  a  thing;  the 
second  to  the  discovery  or  proof  of  the  distinctions  be- 
tween things ;  the  third  to  the  discovery  or  proof  of  in- 
stances and  exceptions;  the  fourth  to  the  discovery,  or 
exclusion,  of  the  different  species  of  genus." 

It  may  be  added  that  the  moods  Cesare  and  Games  - 
tres  are  often  used  in  disproving  a  statement,  because 
they  give  a  universal  negative  conclusion,  founded  upon 
the  exclusion  of  one  class  from  another.  Thus  if  any 
one  were  still  to  assert  that  light  consists  of  material 
particles  it  might  be  met  by  the  following  syllogism : 

"  Material  particles  communicate  impetus  to 

whatever  they  strike, 
Light  does  not  communicate  impetus  to 

whatever  it  strikes ; 
Therefore  light  is  not  material  particles." 

Tike  moods  Baroko  and  Festino  are  less  used,  b* 
iHow  of  a  particular  conclusion  being  established. 

When  we  wish   however  to  establish   objections    Of 


144  THE  IMPERFECT  FIGURES         [LESi 

exceptions  to  a  general  statement,  which  is  indeed  th< 
natural  way  of  meeting  it,  we  employ  the  third  figure, 
The  statement  that  "all  metals  are  solids"  would  al 
once  be  disproved  by  the  exception  mercury ,  as  follows  . 

Mercury  is  not  solid, 
Mercury  is  a  metal ; 
Therefore  some  metal  is  not  solid. 

Were  any  one  to  assert  that  what  is  incomprehensible 
cannot  exist,  we  meet  it  at  once  with  the  argument  that 
Infinity  is  incomprehensible,  but  that  infinity  certainly 
exists,  because  we  cannot  otherwise  explain  the  nature  oi 
a  curve  line,  or  of  a  quantity  varying  continuously ;  there 
fore  something  that  is  incomprehensible  exists.  In  this 
case  even  one  exception  is  sufficient  entirely  to  negative 
the  proposition,  which  really  means  that  because  a  thing 
is  incomprehensible  it  cannot  exist.  But  if  one  incom- 
prehensible thing  does  exist,  others  may  also;  and  all 
authority  is  taken  from  the  statement 

According  to  the  Aristotelian  system  the  third  figure 
must  also  be  employed  whenever  the  middle  term  is  a 
singular  term,  because  in  Aristotle's  view  of  the  subject  a 
singular  term  could  not  stand  as  the  predicate  of  a  pro-    [  \hfi 
position.  >v    A/ 


LESSON  XVIL 

REDUCTION   OF   THE   IMPERFECT   FIGURES 
OF  THE  SYLLOGISM. 

IN  order  to  facilitate  the  recollection  of  the  nineteen  /alid 
and  useful  moods  of  the  syllogism,  logicians  invented,  at 
least  six  centuries  ago,  a  most  curious  system  of  artificial 
words,  combined  into  mnemonic  verses,  which  may  b« 


XVII.]  OF  THE  SYLLOGISM.  14) 

readily  committed  to  memory.  This  device,  however  m« 
genious,  is  of  a  barbarous  and  wholly  unscientific  cha- 
racter ;  but  a  knowledge  of  its  construction  and  use  is  stiD 
expected  from  the  student  of  logic,  and  the  verses  arc 
Aerefore  given  and  explained  below. 

Barbara,  Celarent,  Darii^  /Vrwque,  prioris; 
Cesare,   Camestres,  Festino,  Baroko,  secundae; 
Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 
Bokardo,  Ferison,  habet ;  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

The  words  printed  in  ordinary  type  are  real  Latin 
words,  signifying  that  four  moods  whose  artificial  names 
are  Barbara,  Celarent,  Darii  and  Ferio,  belong  to  the 
first  figure ;  that  four  others  belong  to  the  second ;  six 
more  to  the  third ;  while  the  fourth  figure  moreover 
contains  five  moods.  Each  artificial  name  contains 
three  vowels,  which  indicate  the  propositions  forming 
a  valid  mood ;  thus,  Cte/ArEnt  signifies  the  mood  of  the 
first  figure,  which  has  E  for  a  major  premise,  A  for  the 
minor,  and  E  for  the  conclusion.  The  artificial  words 
altogether  contain  exactly  the  series  of  combinations  of 
vowels  shown  in  p.  140,  excepting  those  in  brackets. 

These  mnemonic  lines  also  contain  indications  of  the 
mode  in  which  each  mood  of  the  second,  third  and  fourth 
figures  can  be  proved  by  reduction  to  a  corresponding 
mood  of  the  first  figure.  Aristotle  looked  upon  the  first 
figure  as  a  peculiarly  evident  and  cogent  form  of  argu- 
ment, the  Dictum  de  omni  et  nvllo  being  directly  ap- 
plicable to  it,  and  he  therefore  called  it  the  Perfect  Figure. 
The  fourth  figure  was  never  recognised  by  him,  and  it  ii 
often  called  the  Oalenian  figure,  because  the  celebrated 
Galen  is  supposed  to  have  discovered  it  The  second 
and  third  figures  were  known  to  Aristotle  as  the  Imperfect 
which  it  was  necessary  to  reduce  to  the  first 


146  THE  IMPERFECT  FIGURES        [L£SS 

figure  by  certain  conversions  and  transpositions  of  UM 
premises,  for  which  directions  are  to  be  found  in  the 
artificial  words.  These  directions  are  as  follows  :  - 

s  indicates  that  the  proposition  denoted  by  the  prc 
ceding  vowel  is  to  be  converted  simply. 

p  indicates  that  the  proposition  is  to  be  converted  p*f 
(ucidttts,  or  by  limitation. 

m  indicates  that  the  premises  of  the  syllogism  are  tc 
be  transposed,  the  major  being  made  the  minor  of  a  new 
syllogism,  and  the  old  minor  the  new  major.  The  m  is 
derived  from  the  Latin  mutare,  to  change. 

JB,  C,  Z>,  F,  the  initial  consonants  of  the  names,  in- 
dicate the  moods  of  the  first  figure,  which  are  produced 
by  reduction;  thus  Cesare,  Camestres  and  Camenes  are 
reducible  to  Celarent,  Darapti,  &c.,  to  Darii,  Fresison  to 
Ferio  and  so  on, 

k  denotes  that  the  mood  must  be  reduced  or  proved 
by  a  distinct  process  called  Indirect  reduction,  or  rtd-uct* 
ad  impossibiU)  which  will  shortly  be  considered. 

Let  us  now  take  some  syllogism,  say  in  Canustrcs,  and 
follow  the  directions  for  reduction.  Let  the  example  be 

All  stars  are  self-luminous    (i) 

All  planets  are  not  self-luminous (2) 

Therefore  no  planets  are  stars (3) 

The  first  s  in  Camestres  shows  that  we  are  to  convert 
simply  the  minor  premise.  The  m  instructs  us  to  change 
the  order  of  the  premises,  and  the  final  s  to  convert  the 
conclusion  simply.  When  all  these  changes  are  made 
we  obtain 

No  self-luminous  bodies  are  planets Converse  of  (a) 

All  stars  are  self-luminous  (i) 

T  herefore  no  stars  are  planets Converse  of  (3) 

This,  it  will  be  found,  is  a  syllogism  in  Celarent  as 
Blight  be  known  from  the  initial  C  in  Camestres. 


OF  THE  SYLLOGISM.  i«> 

As  another  example  let  us  take  Fesapo,  for  instance : 
No  fixed  stars  are  planets, 
All  planets  are  round  bodies  ; 
Therefore  some  round  bodies  are  not  fixev  Stan. 
According  to  the  directions  in  the  name,  we  are  ti 
convert  simply  the  major  premise,  and  by  limitation  the 
minor  premise.    We  have  then  the  following  syllogism  in 
Ferio: 

No  planets  are  fixed  stars, 
Some  round  bodies  are  planets  ; 
Therefore  some  round  bodies  are  not  fixed  stars. 

The  reader  will  easily  apply  the  same  process  of  con- 
version or  transposition  to  the  other  moods,  according  to 
the  directions  contained  in  their  names,  and  the  only 
moods  it  will  be  necessary  to  examine  especially  are 
Bramantip,  Baroko  and  Bokardo.  As  an  example  of 
Bramantip  we  may  take : 

All  metals  are  material  substances, 
All  material  substances  are  gravitating  bodies; 
Therefore  some  gravitating  bodies  are  metals. 
The  name  contains  the  letter  m,  which  instructs  us  to 
transpose  the  premises,  and  the  letter  p,  which  denotes 
conversion  by  limitation ;    effecting  these  changes  wt 
have: 

All  material  substances  are  gravitating  bodies, 
All  metals  are  material  substances ; 
Therefore  some  metals  are  gravitating  bodies. 
This  is  not  a  syllogism  in  Barbara,  as  we  might  hav* 
expected,   but   is  the  weakened   mood  AAI  of  the  first 
figure    It  is  evident  that  the  premises  yield  the  conclusion 
*  all  metals  are  gravitating  bodies,"  and  we  must  take  the 
letter  p  to  indicate  in  this  mood  that  the  conclusion  is 
weaker  than  it  might  be.     In  truth  the  fourth  figure  is  M 

IO— 2 


148  THE  IMPERFECT  FIGURES         [LES 

imperfect  and  unnatural  in  form,  containing  nothing  but 
ill-arranged  syllogisms,  which  would  have  been  bettci 
itated  in  the  first  figure,  that  Aristotle,  the  founder  of 
logical  science,  never  allowed  the  existence  of  the  figure 
at  all.  It  is  to  be  regretted  that  so  needless  an  addition 
pras  made  to  the  somewhat  complicated  forms  of  the 
syllogism. 

Indirect  reduction.  The  moods  Baroko  and  Bokardo 
give  a  good  deal  of  trouble,  because  they  cannot  be  re- 
duced directly  to  the  first  figure.  To  show  the  mode  of 
treating  these  moods  we  will  take  X,  K,  Zto  represent  the 
major,  middle  and  minor  terms  of  the  syllogism,  and 
Baroko  may  then  be  stated  as  follows : 

All  X's  are  K>s, 
Some  Z's  are  not  V* ; 
Therefore          Some  Z's  are  not  ^'s. 

Now  if  we  convert  the  major  premise  by  Contrapo- 
sition (p.  83)  we   have   "all  not-ys  are  not-A^'s,"  and, 
making  this  the  major  premise  of  the  syllogism,  we  have 
All  not-  K*s  are  not  X\ 
Some  Z's  are  not-  X1* ; 
Therefore          Some  Z's  are  not  X's. 

Although  both  the  above  premises  appear  to  be  nega- 
tive, this  is  really  a  valid  syllogism  in  Ferio,  because 
two  of  the  negative  particles  merely  affect  the  middl* 
term  (see  p.  134),  and  we  have  therefore  effected  the  re 
Auction  of  the  syllogism. 

Bokardo,  when  similarly  stated,  is  as  follows ; 

Some  y*  are  not  A*'s, 
All  rsareZ'f; 
Therefore          Some  Z's  are  not  Jfs. 


OF  THE  SYLLOGISM.  149 

To  reduce  this,  convert  the  major  pre/nise  by  nega- 
tion, and  then  transpose  the  premises.    V/e  have: 
All  X's  are  Z's, 
Some  not-A^s  are  K's; 
Therefore          Some  not-Jf's  are  Z's. 

This  conclusion  is  the  converse  by  negation  of  the 
lormer  conclusion,  the  truth  of  which  is  thus  proved  by 
reduction  to  a  syllogism  in  Darii. 

Both  these  moods,  Baroko  and  Bokardo,  may  however 
be  proved  by  a  peculiar  process  of  Indirect  reduction, 
closely  analogous  to  the  indirect  proofs  often  employed  by 
Euclid*  in  Geometry.  This  process  consists  in  supposing 
the  conclusion  of  the  syllogism  to  be  false,  and  its  con- 
tradictory therefore  true,  when  a  new  syllogism  can  easily 
be  constructed  which  leads  to  a  conclusion  contradictory 
of  one  of  the  original  premises.  Now  it  is  absurd  in  logic 
to  call  in  question  the  truth  of  our  own  premises,  for  the 
very  purpose  of  argument  or  syllogism  is  to  deduce  a  con- 
clusion which  will  be  tiue  when  the  premises  are  true. 
The  syllogism  enables  us  to  restate  in  a  n»w  form  the  in- 
formation which  is  contained  in  the  premises,  just  as  a 
machine  may  deliver  to  us  in  a  new  form  the  material 
which  is  put  into  it  The  machine,  or  rather  the  maker 
of  the  machine,  is  not  responsible  for  the  quality  of  the 
materials  furnished  to  it,  and  similarly  the  logician  is  not 
responsible  in  the  least  for  the  truth  of  his  premises,  but 
only  for  their  correct  treatment.  He  must  treat  them,  if 
he  treat  them  at  all,  as  true ;  and  therefore  a  conclusion 
which  requires  the  falsity  of  one  of  our  premises  is  alto- 
gether absurd. 

To  apply  this  method  we  may  take  Baroko,  at  bo 
(ore: 

AllJTsare  K's (l) 

Some  2Ts  are  not  K's  (2) 

Therefore        Some  Z's  are  not  JCs (j> 


150  THE  IMPERFECT  FIGURES        [LSS& 

If  this  conclusion  be  not  true  then  its  contradictory, 
'aflZ's  are  A'V  must  of  necessity  be  regarded  as  true 
(pp.  76 — 79).  Making  this  the  minor  premise  of  a  new 
syllogism  with  the  original  major  premise  we  have : 

All  JTs  are  K>s (i) 

All  Z*s  are  X's contradictory  of  £3) 

Htnce        All  Z*s  are  XV 

Now  this  conclusion  in  A,  is  the  contradictory  of  our  old 
minor  premise  in  0,  and  we  must  either  admit  one  of  our 
own  premises  to  be  false  or  allow  that  our  original  con- 
clusion is  true.  The  latter  is  of  course  the  alternative 
we  choose, 

We  treat  Bokardo  in  a  very  similar  manner ; 

Some  X*s  are  not  A?s (i) 

All  K's  are  Z>s (2) 

Therefore         Some  Z's  are  not  X*s (3) 

If  this  conclusion  be  not  true  then  '  all  Z*s  are  X*s '  must 

be  true.    Now  we  can  make  the  syllogism  : 

All  Z*s  are  X*s Contradictory  of  (3) 

All  rs  area's  (2) 

Hence    All  Fs  are  A"s. 

This  conclusion  is  the  contradictory  of  (i),  the  original 
major  premise,  and  as  this  cannot  be  allowed,  we  must 
either  suppose  (2)  the  original  minor  premise  to  be  false, 
which  is  equally  impossible,  or  allow  that  our  origina) 
conclusion  is  true. 

It  will  be  observed  that  in  both  these  cases  of  Indireci 
Reduction  or  Proof  we  use  a  syllogism  in  Barbara,  which 
fact  is  indicated  by  the  initial  letters  of  Baroko  and  Bo- 
kardo. The  same  process  of  Indirect  proof  may  ta 
applied  to  any  of  the  other  moods,  but  it  is  not  usual  to 
do  so  as  the  simpler  process  of  direct  or  as  it  is  often 
called  ostensive  reduction  is  sufficient 


•ml  Of   THE  SYLLOGISM.  151 

It  will  be  remembered  that  when  in  Lesson  xv.  /p.  135) 
we  considered  the  rules  of  the  syllogism,  there  were  two 
supplementary  rules,  the  7th  and  8th,  concerning  particu 
Ur  premises,  which  were  by  no  means  of  a  self-evident 
character,  and  which  require  to  be  proved  by  the  six  more 
fundamental  rules.  We  have  now  sufficiently  advanced 
to  consider  this  proof  with  advantage.  The  7th  rule 
forbids  us  to  draw  any  conclusion  from  two  particular  pre- 
mises ;  now  such  premises  must  be  either  n,  10,  01,  or  00. 
Of  these  n  contain  no  distributed  term  at  all,  so  that  the 
3rd  rule,  which  requires  the  middle  term  to  be  distributed, 
must  be  broken.  The  premises  00  evidently  break  the 
5th  rule,  against  negative  premises.  The  conclusion  oi 
the  pair  10  must  be  negative  by  the  6th  rule,  because  one 
premise  is  negative;  the  major  term  therefore  will  be 
distributed,  but  as  the  major  premise  is  a  particular 
affirmative  it  cannot  be  distributed  without  committing 
the  fallacy  of  illicit  process  of  the  major,  against  rule  4. 
Lastly  the  premises  01  contain  only  one  distributed  term, 
the  predicate  of  the  major  premise.  But  as  the  conclusion 
must  be  negative  by  rule  6th,  the  major  term  must  be 
distributed :  we  oagnt  to  have  then  in  the  premises  two 
distributed  terms,  one  for  the  middle  term,  the  other  for 
the  major  term ;  but  as  the  premises  contain  only  a  single 
distributed  term,  we  must  commit  the  fallacy  either  ol 
undistributed  middle  or  of  illicit  process  of  the  major 
term,  if  we  attempt  to  draw  any  conclusion  at  all  We 
thus  see  that  in  no  possible  case  can  a  pair  of  particular 
premises  give  a  valid  conclusion. 

The  8th  rule  of  the  syllogism  instructs  us  that  if  one 
premise  of  a  syllogism  be  particular  the  conclusion  must 
•Iso  be  p:\rticular.  It  can  only  be  shown  to  be  true  by 
going  over  all  the  possible  cases  and  observing  that  the 
six  princip;d  rules  of  the  syllogism  always  require  the 
conclusion  ;c  be  particular.  Suppose  for  inttance  the 


152          IRREGULAR  AND  COMPOUND      <LES* 

premises  are  A  and  I ;  then  they  contain  only  one  di» 
tributed  term,  the  subject  of  A,  and  this  is  required  foi 
the  middle  term  by  rule  3.  Hence  the  minor  term  cannot 
be  distnbuted  without  breaking  rule  4,  so  that  the  con- 
dusion  must  be  the  proposition  I.  The  premises  AO  would 
xmtain  two  distributed  terms,  the  subject  of  A  and  the 
predicate  of  0;  but  if  we  were  to  draw  from  them  the 
conclusion  B,  the  major  and  minor  terms  would  require 
to  be  distributed,  so  that  the  middle  term  would  remain 
undistributed  against  rule  3.  The  reader  can  easily  prove 
the  other  cases  such  as  El  by  calculating  the  number  of 
distributed  terms  in  a  similar  manner:  it  will  always  be 
found  that  there  are  insufficient  terms  distributed  in  the 
premises  to  allow  of  a  universal  conclusion. 


/A  LESSON   XVIII. 

V  IRREGULAR    AND    COMPOUND    SYLLOGISMS. 

IT  may  seem  surprising  that  arguments  which  are  met 
with  in  books  or  conversation  are  seldom  or  never  thrown 
into  the  form  of  regular  syllogisms.  Even  it  a  complete 
syllogism  be  sometimes  met  with,  it  is  generally  employed 
in  mere  affectation  of  logical  precision.  In  former  cen- 
turies it  was,  indeed,  the  practice  for  all  students  at  the 
Universities  to  take  part  in  public  disputations,  during 
which  elaborate  syllogistic  arguments  were  put  forward 
by  one  side  and  confuted  by  precise  syllogisms  on  the 
>ther  side.  This  practice  has  not  been  very  long  dis- 
xmtinued  at  the  University  of  Oxford,  and  is  said  to  be 
•till  maintained  in  some  continental  Universities;  but 
except  in  such  school  disputations  it  must  be  allowed  that 
perfectly  formal  syllogisms  are  seldom  employed. 


<vni.]  ^SfLLOGISMS.  153 

In  truth,  however,  it  is  not  syllogistic  arguments  which 
are  wanting ;  wherever  any  one  of  the  conjunctions, 
therefore,  because,  for,  since,  hence,  inasmuch  as,  cons* 
qutntly  occurs,  it  is  certain  that  an  inference  is  being 
drawn,  and  this  will  very  probably  be  done  by  a  true 
syllogism.  It  is  merely  the  complete  statement  of  the 
jremises  and  conclusion,  which  is  usually  neglected  be« 
i  ause  the  reader  is  generally  aware  of  one  or  other  of  the 
premises,  or  he  can  readily  divine  what  is  assumed ;  and 
it  is  tedious  and  even  offensive  to  state  at  full  length  what 
the  reader  is  already  aware  o£  Thus,  if  I  say  "atmo- 
spheric air  must  have  weight  because  it  is  a  material 
substance,"  I  certainly  employ  a  syllogism ;  but  I  think 
it  quite  needless  to  state  the  premise,  of  which  I  clearly 
assume  the  truth,  that  "  whatever  is  a  material  substance 
has  weight."  The  conclusion  of  the  syllogism  is  the  first 
proposition,  viz.  "atmospheric  air  has  weight."  The 
middle  term  is  "  material  substance,"  which  does  not  occur 
in  the  conclusion;  the  minor  is  "atmospheric  air,"  and  the 
major,  "having  weight."  The  complete  syllogism  is  evi- 
dently : 

All  material  substances  have  weight, 
Atmospheric  air  is  a  material  substance ; 
Therefore  atmospheric  air  has  weight 
This  is  in  the  very  common  and  useful  mood  Barbara. 

A  syllogism  when  incompletely  stated  is  usually  called 
an  en&Tjneme,  and  this  name  is  often  supposed  to  be 
derived  from  two  Greek  words  («V,  in,  and  dvpor,  mind), 
so  as  to  signify  that  some  knowledge  is  held  by  the  mind 
and  is  supplied  in  the  form  of  a  tacit,  that  is  a  silent  or 
understood  premise.  Most  commonly  this  will  be  the 
major  premise,  and  then  the  enthymeme  may  be  said  to 
be  of  theTirst  Order.  Less  commonly  the  minor  premise 
is  unexpressed,  'and  the  enthvmeme  is  of  the  Second 


154  IRREGULAR  AND  COMPOUND     [LKS& 

Order.  Of  this  nature  is  the  following  argument: 
u  Comets  must  be  subject  to  the  law  of  gravitation ;  foi 
this  is  true  of  all  bodies  which  move  in  elliptic  orbits," 
It  is  so  clearly  implied  that  comets  move  in  elliptic  orbits, 
that  it  would  be  tedious  to  state  this  as  the  minor  premise 
in  a  complete  syllogism  of  the  mood  Barbara,  thus  : 

All  bodies  moving  in  elliptic  orbits  are  subject  to 

the  law  of  gravitation  ; 
Comets  move  in  elliptic  orbits ; 
Therefore  comets  are  subject  to  the  law  of  gravitation, 

It  may  happen  occasionally  that  the  conclusion  of  a 
syllogism  is  left  unexpressed,  and  the  enthymeme  may  then 
hie  said  to  belong  to  the  Third  Order.  This  occurs  in  the 
case  of  epigrams  or  other  witty  sayings,  of  which  the  very 
wit  often  consists  in  making  an  unexpressed  truth  ap- 
parent. Sir  W.  Hamilton  gives  as  an  instance  of  this 
kind  of  enthymeme  the  celebrated  epigram  written  by 
Person  the  English  scholar  upon  a  contemporary  German 
scholar: 

"The  Germans  in  Greek 

Are  sadly  to  seek ; 

Not  five  in  five  score, 

But  ninety-five  more ; 

All,  save  only  Hermann, 

And  Hermann's  a  German." 

It  is  evident  that  while  pretending  to  make  an  exception 
of  Hermann,  the  writer  ingeniously  insinuates  that  since 
he  is  a  German  he  has  not  a  correct  knowledge  of  Greek. 
The  wonderful  speech  of  Antony  over  the  body  of  Caesar, 
kn  Shakspeare's  greatest  historical  play,  contains  a  series 
of  syllogistic  arguments  of  which  the  conclusions  arc 
suggested  only. 

Even  a  single  proposition  may  have  a  syllogistic  force 
tf  it  clearly  suggest  to  the  mind  a  second  premise  which 


xvm.J  SYLLOGISMS.  155 

thus  enables  a  conclusion  to  be  drawn.  The  expression 
of  Home  Tooke,  "  Men  who  have  no  rights  cannot  justly 
complain  of  any  wrongs,"  seems  to  be  a  case  in  point ;  foi 
there  are  few  people  who  have  not  felt  wronged  at  some 
time  or  other,  and  they  would  therefore  be  likely  to  argot 
whether  upon  true  or  false  premises,  as  follows : 

Men  who  have  no  rights  cannot  justly  complain  oJ 

any  wrongs; 
We  can  justly  complain; 
Therefore  we  are  not  men  who  have  no  rights. 
In  other  words,  we  have  rights. 

Syllogisms  may  be  variously  joined  and  combined 
together,  and  it  is  convenient  to  have  special  names  for 
the  several  parts  of  a  complex  argument  Thus  a  syllo- 
gism which  proves  or  furnishes  a  reason  for  one  of  the 
premises  of  another  syllogism  is  called  a  Prosylloglam; 
and  a  syllogism  which  contains  as  a  premise  me  concUP* 
•ion  of  another  syllogism  is  called  an  BpUyllOflam. 

Take  the  example : 

All  ^s  are  A\ 

And  all  (7s  are  ff*\     ^  ^ 


Therefore  all  (7s  are  At*. 

But  all  //s  are  (7s; 


Therefore  All  /7s  are  A'*. 


This  evidently  contains  two  syllogisms  in  the  mood  Bar 
bara,  the  first  of  which  is  a  Prosyllogism  with  respect  tc 
the  second,  while  the  second  is  an  Episyllogism  witk 
respect  to  the  first 

The  peculiar  name  EpJgheirema  is  given  to  a  syllogism 
when  either  premise  is  proved  or  supported  by  a  reasoa 
implying  the  existence  of  an  i  expressed  pro 

syllogism  ;  thus  the  form, 


156          IRREGULAR  AND  COMPOUND     [LES& 

All  ffs  are  A's,  for  they  arc  /"s, 
And  all  Cs  are  ffs,  for  they  are  Qs ; 
Therefore  all  C's  are  ^4's, 

is  a  double  Epicheirema,  containing  reasons  for  bot), 
premises.  The  reader  will  readily  decompose  it  into 
three  complete  syllogisms  of  the  mood  Barbara. 

A  more  interesting  form  of  reasoning  is  found  in  the 
chain  of  syllogisms  commonly  called  the  Sorites,  from  the 
Greek  word  <ro>por,  meaning  heap.  It  is  usually  stated  in 
this  way : 

All  A's  are  &s, 
All  0s  are  Cs, 
All  Cs  are  /?$, 
All  &s  are  £?*  ; 
Therefore  all  A*  s  are  .fs. 

The  chain  can  be  carried  on  to  any  length  provided  it  is 
perfectly  consecutive,  so  that  each  term  except  the  first 
and  last  occurs  twice,  once  as  subject  and  once  as  predi- 
cate. It  hardly  needs  to  be  pointed  out  that  the  sorites 
really  contains  a  series  of  syllogisms  imperfectly  ex- 
pressed; thus 

First  Syllogism.     Second  Syllogism.     Last  Syllogism, 
^s  are  Cs,  Cs  are  /7s,  D>s  are  ^s, 

A's  are  ffs ;  A's  are  (7s;  A's  are  Z?'s ; 

.'.  A's  are  Cs.         /.  A's  are  Z7s.  .-.  A's  are  E's. 

Each  syllogism  furnishes  a  premise  to  the  succeeding  one, 
of  which  it  is  therefore  the  prosyllogism,  and  any  syllo- 
gism may  equally  be  considered  the  episyllogism  of  that 
which  precedes. 

In  the  above  sorites  all  the  premises  were  univenal 
and  affirmative,  but  a  sorites  may  contain  one  particular 
premise  provided  it  be  the  first,  and  one  negative  premise 
provided  it  be  the  last  The  reader  may  easily  assure 
himself  by  trial,  that  if  any  premise  except  the  first  wew 


xnil.]  SYLLOGISMS.  157 

particular  the  fallacy  of  undistributed  middle  would  be 
committed,  because  one  of  the  middle  terms  would  be  the 
predicate  of  one  affirmative  premise  and  the  subject  of 
another  particular  premise.  If  any  premise  but  the  last 
arere  negative  there  would  be  a  fallacy  of  illicit  process  o* 
the  major  term. 

It  is  not  to  be  supposed  that  the  forms  of  the  syllogisir 
hitherto  described  are  all  the  kinds  of  reasoning  actuall) 
employed  in  science  or  common  life.  In  addition  to  the 
hypothetical  and  disjunctive  syllogisms  and  some  othei 
forms  to  be  described  in  succeeding  lessons,  there  are 
really  many  modes  of  reasoning  of  which  logicians  hare 
not  taken  much  notice  as  yet.  This  was  clearly  pointed 
out  more  than  two  hundred  years  ago  by  the  writers  ol 
the  Port  Royal  Logic  )  a  work  first  printed  in  the  year  1662, 
but  which  has  been  since  reprinted  very  often  and  trans- 
lated into  a  great  many  languages.  The  book  is  named 
from  a  place  near  Paris  where  a  small  religious  com- 
munity lived,  of  which  the  authors  of  the  book,  namely 
Arnauld  and  Nicole,  and  a  contributor  to  it  the  great 
philosopher  and  mathematician  Pascal,  were  the  most 
celebrated  members.  The  Port  Royal  Logic  was  to  a 
considerable  extent  the  basis  of  the  well-known  Watts' 
Logic,  but  the  reader  can  now  be  referred  to  an  admirable 
translation  of  the  original  work  made  by  Professor  Spencer 
Bayn*s,  of  St  Andrew's. 

Many  improvements  of  Logic  may  be  found  in  thii 
work,  such  as  the  doctrine  of  Extension  and  Intension 
explained  in  Lesson  V.  In  the  9th  Chapter  of  the  3rd 
Part  moreover  it  is  wisely  pointed  out  that  "little  pains 
are  taken  in  applying  the  rules  of  the  syllogism  to  reason- 
Ings  of  which  the  propositions  are  complex,  though  thii 
is  often  very  difficult,  and  there  are  many  arguments  of 
this  nature  which  appear  bad,  but  which  are  nevertheless 
very  good;  and  besides,  the  use  of  such  reasonings  if 


A  A 


158  IRREGULAR  AND  COMPOUND     [LE88 

much  more  frequent  than  that  of  syllogisms  which  art 
quite  simple."  Some  examples  are  given  of  the  complex 
syllogisms  here  referred  to;  thus: 

The  sun  is  a  thing  insensible, 

The  Persians  worship  the  sun ; 

Therefore  the  Persians  worship  a  thing  insensible. 

Phis  is  an  argument  which  cannot  be  proved  by  the  rule* 
of  the  syllogism,  and  yet  it  is  not  only  evidently  true,  but 
is  an  exceedingly  common  land  of  argument  Another 
example  is  as  follows : 

The  Divine  Law  commands  us  to  honour  kings ; 

Louis  XIV.  is  a  long ; 

Therefore  the  Divine  Law  commands  us  to  honour 

Louis  XIV. 

The  reader  will  also  find  that  arguments  which  are 
really  quite  valid  and  syllogistic  are  expressed  in  language 
so  that  they  appear  to  have  four  distinct  terms  and  thus  to 
break  one  of  the  rules  of  the  syllogism.     Thus  if  I  say 
"  Diamonds  are  combustible,  for  they  are  composed  of 
carbon  and  carbon  is  combustible,"  there  are  four  terms 
employed,  namely,  diamonds,  combustible,  composed  ol 
carbon,  and  carbon.     But  it  is  easy  to  alter  the  construc- 
tion of  the  propositions  so  as  to  get  a  simple  syllogism 
without  really  altering  the  sense,  and  we  then  have : 
What  is  composed  of  carbon  is  combustible ; 
Diamonds  are  composed  of  carbon  ; 
Therefore  diamonds  are  combustible. 
Examples  are  given  at  the  end  of  the  book  of  concise 
irguments,  taken  from  Bacon's  Essays  and  other  writings, 
which  the  student  can  reduce  to  the  syllogistic  form  by 
easy  alterations  ;  but  it  should  be  clearly  understood  that 
these  changes  are  of  an  extra-logical  character,  and  belong 
more  properlv  to  the  science  of  language. 


JLVIII.J  SYLLOGISMS.  ift 

I  may  here  explain  that  the  syllogism  and  the  soritei 
can  be  expressed  either  in  the  order  of  extension  or  that 
of  intension.  In  regard  to  the  number  of  individual 
things  the  noble  metals  are  part  of  the  metals,  and  thr 
metals  are  part  of  the  elements ;  but  in  regard  to  in- 
tension, that  is  to  say  the  qualities  implied  in  the  names, 
element  is  part  of  metal,  and  metal  is  part  of  noble  metal. 
So  again  in  extension  the  genus  of  plants  Anemone  is 
part  of  the  order  Ranunculaceas,  and  this  is  part  oi 
the  great  class  Exogens;  but  in  intension  the  cha- 
racter of  Exogen  is  part  of  the  character  of  Ranuncu- 
laceae,  and  this  is  part  of  the  character  of  Anemone. 
Syllogistic  reasoning  is  equally  valid  and  evident  in  either 
case,  and  we  might  represent  the  two  modes  in  ordinary 
language  as  follows : 

Extensive  Syllogism. 
All  Ranunculaceae  are  Exogens ; 
The  Anemone  is  one  of  the  Ranunculaceae ; 
Therefore  the  Anemone  is  an  Exogen. 

Intensive  Syllogism. 
All  the  qualities  of  Ranunculaceae  are  qualities  of 

Anemone ; 

All  the  qualities  of  Exogen  are  qualities  of  Ranun- 
culaceae ; 
Therefore  all  the  qualities  of  Exogen  are  qualities  of 

Anemone. 

Any  sorites  can  be  similarly  represented  either  in  ex- 
.ension  or  intension. 

Concerning  the  Aristotelian  doctrine  of  the  Enthy 
meme,  see  Mansel's  Aldrich,  App.  Note  F,  and  Hamil- 
ton's Lectures  on  Logic,  Lecture  xx.  Port  Royal  Logic^ 
translated  by  T.  Spencer  Baynes,  5th  ed.  Edinburgh 
l86l, 


cto  .  Of  CONDITIONAL 


LESSON   XIX. 
OF   CONDITIONAL  ARGUMENTS. 

i  T  will  be  remembered  that  when  treating  of  proposition. 
<re  divided  them  into  two  distinct  kinds,  Categorical  Pro- 
positions, and  Conditional  Propositions.  The  former  kind 
alone  has  hitherto  been  considered,  and  we  must  now 
proceed  to  describe  Conditional  propositions  and  the  ar- 
guments which  may  be  composed  of  them. 

Logicians  have  commonly  described  Conditional  pro- 
positions as  compose4  of  two  or  more  Categorical  pro- 
positions united  by  a  conjunction.  This  union  may 
happen  in  two  ways,  giving  rise  to  two  very  different 
species  of  conditionals,  which  we  shall  call  Hypothetical 
Propositions  and  Disjunctive  Propositions.  The  way  in 
which  the  several  kinds  of  propositions  are  related  will 
be  seen  in  the  following  diagram  : 

{-Categorical 
Propositions  are  j  Hypothetical 


A  conditional  proposition  may  be  further  described 
as  one  which  makes  a  statement  under  a  certain  con- 
dition or  qualification  restricting  its  application.  In  the 
hypothetical  form  this  condition  is  introduced  by  the 
conjunction  if,  or  some  other  word  equivalent  to  it 
Thus— 

"  If  iron  is  impure,  it  is  brittle  " 

is  a  hypothetical  proposition  consisting  of  two  distinct 
categorical  propositions,  the  first  of  which,  "  Iron  is  im- 
pure,'' is  called  the  Antecedent;  the  second,  "  It  is  brittle.* 


'V* 
H 


XIX.] 


ARGUMENTS. 


the  Consequent.  In  this  case  "  impurity"  it  the  condition 
or  qualification  which  limits  the  application  of  the  pre-X 
dicate  brittle  to  iron.  It  was  asserted  by  Home  Tooke  in?  v\  ; 
his  celebrated  work  The  Diversions  of  Purley^  that  all 
conjunctions  are  the  remains  or  corrupted  forms  of  verbs. 
Fhis  is  certainly  true  in  the  case  of  the  hypothetical  con. 
/unction  ;  for  the  word  if  in  old  English  is  written  gif,  01 
gyfy  and  is  undoubtedly  derived  from  the  verb  to  give. 
We  may  actually  substitute  at  present  any  verb  of  similar 
meaning,  as  for  instance — grant,  allow,  suppose.  Thus 
jre  may  say — 

u  Grant  that  iron  is  impure,  and  it  is  brittle." 
u  Supposing  that  iron  is  impure,  it  is  brittle." 
The  hypothetical  proposition  might  be  employed  in 
arguments  of  various  form,  but  only  two  of  these  are  ol 
sufficient  importance  to  receive  special  names.  The  hy- 
pothetical syllogism  consists  of  two  premises,  called  the 
major  and  minor,  as  in  the  case  of  the  ordinary  syllo- 
gism. The  major  premise  is  hypothetical  in  form ;  the 
minor  premise  is  categorical,  and  according  as  it  is  af- 
firmative or  negative  the  argument  is  said  to  be  a  Construc- 
tive or  a  Destructive  hypothetical  syllogism.  Thus  the  form, 

If  A  is  By  C  is  Z>; 

But  A  is  B\ 

Therefore  C  is  Z>, 
is  a  constructive  hypothetical  syllogism. 

It  must  be  carefully  observed  that  the  minor  premise 
affirms  the  antecedent  of  the  major  premise,  whence  the 
argument  is  said  to  be  of  the  modus  ponens,  or  mood 
which  posits  or  affirms.  It  is  probably  one  of  the  most 
familiar  and  common  kinds  of  argument.  The  form, 

If  A  is  Bt  Cii  D\ 

But  C  is  not  D ; 
PV       Therefore  A  is  not  B. 


OF  CONDITIONAL 


represents  the  corresponding  Destructive  hypothetic*. 
•yUoglsm,  also  called  the  modus  tollens,  or  the  mood 
which  removes  the  consequent.  It  must  be  carefully  ob- 
served again  that  it  is  the  consequent,  not  the  antecedent. 
which  is  denied. 

The  only  rule  which  is  requisite  for  testing  the  validity 
of  such  syllogisms  embodies  what  we  have  observed 
above  ;  viz.  tRat  either  the  antecedent  must  be  affirmed^  ^ 
9r  the  consequent  denied.  If  either  part  of  this  rule  be 
broken,  a  serious  fallacy  will  be  committed.  Thus  the 
apparent  argument, 

HA  is*,  CisZ?; 

But  C  is  D  ;   ^$     £-  «^    ~^o~*    —* 

Therefore  A  is  B, 

is  really  a  fallacy  which  we  may  call  the  fallacy  of  affirm* 
ing  the  consequent,  and  its  fallacious  nature  is  readily  un- 
derstood by  reflecting  that  "  A  being  B  *  is  not  stated  to 
be  the  only  condition  on  which  C  is  D.  It  may  happen 
that  when  £  is  F,  or  G  is  ff,  or  under  a  hundred  other 
circumstances,  C  is  D,  so  that  the  mere  fact  of  C  being  D 
is  no  sufficient  proof  that  A  is  B.  Thus,  if  a  man's  cha- 
racter be  avaricious  he  will  refuse  to  give  money  for  usefui 
purposes  ;  but  it  does  not  follow  that  every  person  who 
refuses  to  give  money  for  such  purposes  is  avaricious. 
There  may  be  many  proper  reasons  or  motives  leading 
liim  to  refuse  ;  he  may  have  no  money,  or  he  may  con- 
sider the  purpose  not  a  useful  one,  or  he  may  have  more 
useful  purposes  in  view. 

A  corresponding  fallacy  arises  from  denying  tk<  3*4+ 
«M**4  as  in  the  form— 

If  A  is  B,  Cis  D\ 

But  A  is  not  B  ; 
Therefore  C  is  not  /X 


XIX]  ARGUMENTS.  16* 

The  error  may  be  explained  in  the  same  way;  foi  as 
"A  being  Bn  is  not  stated  to  be  the  only  condition  of 
C  being  D,  we  may  deny  this  one  condition  to  be  true 
but  it  is  possible  that  the  consequent  may  happen  to  be 
true  for  other  reasons,  of  which  we  know  nothing.  Thus 
if  a  man  is  not  avaricious  we  cannot  conclude  that  he  will 
be  sure  to  give  money  whenever  asked.  Or  take  the  fol- 
lowing example : 

"If  the  study  of  Logic  furnished  the  mind  with  a  multi- 
tude of  useful  facts  like  the  study  of  other  sciences,  it 
would  deserve  cultivation;  but  it  does  not  furnish  the 
mind  with  a  multitude  of  useful  facts;  therefore  it  does 
not  deserve  cultivation." 

This  is  evidently  a  fallacious  argument,  because  the 
acquiring  of  a  multitude  of  useful  facts  is  not  the  only 
ground  on  which  the  study  of  a  science  can  be  recom- 
mended. To  correct  and  exercise  the  powers  of  judgment 
and  reasoning  is  the  object  for  which  Logic  deserves  to 
be  cultivated,  and  the  existence  of  such  other  purpose  is 
ignored  in  the  above  fallacious  argument,  which  evidently 
involves  the  denial  of  the  antecedent. 

Although  it  is  usual  in  logical  works  to  describe  the 
hypothetical  proposition  and  syllogism  as  if  they  were 
different  in  nature  from  the  categorical  proposition  and 
syllogism,  yet  it  has  long  been  known  that  the  hypo- 
theticals  can  be  reduced  to  the  categorical  form,  and 
brought  under  the  ordinary  rules  of  the  syllogism.  As  a 
general  rule  the  hypothetical  proposition  can  be  readily 
converted  into  a  universal  affirmative  proposition  (A)  of 
exactly  the  same  meaning.  Thus  our  instance,  "If iron 
is  impure,  it  is  brittle,"  becomes  simply  "Impure  iron  is 
brittle."  In  making  this  alteration  in  a  hypothetical  syl- 
logism it  will  be  found  necessary  to  supply  a  new  minoi 
term;  thus  m  the  case, 

II— 2 


<04  OF  CONDITIONAL  I 

If  iron  is  impure  it  is  brittle ; 
But  it  is  impure ; 
Therefore  it  is  brittle, 

ire   have  to  substitute  for  the  indefinite  pronoun  </,  tht 
it  OK  in  question,  and  we  obtain  a  correct  categorical  syl- 
logism in  the  mood  Barbara : 
Impure  iron  is  brittle  ; 
The  iron  in  question  is  impure  iron  ; 
Therefore  the  iron  in  question  is  brittle. 
Sometimes  the  reduction  requires  a  more  extensive 
change  of  language.     For  instance, 

If  the  barometer  is  falling,  bad  weather  is  coming ; 
But  the  barometer  is  falling ; 
Therefore  bad  weather  is  coming, 
may  be  represented  in  the  following  form : 
The  circumstances  of  the  barometer  falling  are  the  cir- 
cumstances of  bad  weather  coming  ; 
But  these  are  the  circumstances  of  the  barometer  fall* 

ing; 
Therefore  these  are  the  circumstances  of  bad  weathei 

coming. 

As  an  instance  of  the  Destructive  Hypothetical  syl- 
logism we  may  take : 

If  Aristotle  is  right,  slavery  is  a  proper  form  of  society; 
But  slavery  is  not  a  proper  form  of  society; 
Therefore  Aristotle  is  not  right 

This  becomes  as  a  categorical : 
The  case  of  Aristotle  being  right  is  the  case  of  slaver? 

being  a  proper  form  of  society; 
But  this  is  not  the  case  ; 
Therefore  this  is  not  the  case  of  Aristotle  being  right 

If  not  reducible  by  any  other  form  of  expression,  hypo* 
tketicals  can  always  be  reduced  by  the  use  of  the  wordi 


XIX.]  ARGUMENTS.  165 

It  will  now  be  easily  made  apparent  that  the  fallacy  ol 
affirming  the  consequent  is  really  a  breach  of  the  3rd 
rule  of  the  syllogism,  leading  to  an  undistributed  middle 
term.  Our  example  may  be  as  before : 

If  a  man  is  avaricious  he  will  refuse  money ; 
But  he  does  refuse  money  ; 
Therefore  he  is  avaricious. 
This  becomes  as  a  categorical  syllogism. 
All  avaricious  men  refuse  money; 
But  this  man  refuses  money ; 
Therefore  this  man  is  avaricious. 
This  is  the  mood  AAA  in  the  second  figure ;  and  the 
raddle  term,  refusing  money,  is  undistributed  in  both 
premises,  so  that  the  argument  is  entirely  fallacious. 

Again,  the  fallacy  of  denying  the  antecedent  is  equiva- 
lent to  the  illicit  process  of  the  major.  Our  former 
example  (p.  163)  may  thus  be  represented: 

"A  science  which  furnishes  the  mind  with  a  multitude 
of  useful  facts  deserves  cultivation ;  but  Logic  is  not  such 
a  science ;  therefore  Logic  does  not  deserve  cultivation." 
This  apparent  syllogism  is  of  the  mood  ABE  in  the 
first  figure,  which  breaks  the  fourth  rule  of  the  syllogism, 
because  the  major  term,  deserving  cultivation,  is  dis 
tributed  in  the  negative  conclusion,  but  not  in  the  affirma- 
tive major  premise. 

We  now  pass  to  the  consideration  of  the  disjunctive 
proposition,  which  instead  of  a  single  predicate  has 
several  alternatives  united  by  the  disjunctive  conjunction 
or,  any  one  of  which  may  be  affirmed  of  the  subject  "A 
member  of  the  House  of  Commons  is  either  a  representa- 
tive of  a  county,  or  of  a  borough,  or  of  a  University,"  is  an 
instance  of  such  a  proposition,  containing  three  alterna- 
tives ;  but  there  may  be  any  number  of  alternatives  frotr 
two  upwards. 


. 


166  OF  CONDITIONAL  [LESS 

The  disjunctive  gylloglHm  consists  of  a  disjunctive 
major  premise  with  a  categorical  proposition,  either  af- 
firmative or  negative,  forming  the  minor  premise.  Thu  . 
arise  two  moods,  of  which  the  affirmative  mood  is  callec 
by  the  Latin  words  modus  ponendo  fallens  (the  mood 
which  by  affirming  denies),  and  may  be  thus  stated : 

A  is  either  B  or  C, 

But  A  is  B ; 

Therefore  A  is  not  C. 

This  form  of  argument  proceeds  on  the  supposition 
that  if  one  alternative  of  a  disjunctive  proposition  be  held 
true,  the  others  cannot  also  be  true.  Thus  "  the  time  of 
year  must  be  either  spring,  summer,  autumn  or  winter," 
and  if  it  be  spring  it  cannot  be  summer,  autumn  or  winter ; 
and  so  on.  But  it  has  been  objected  by  Whately,  Man- 
sel,  Mill,  as  well  as  many  earlier  logicians,  that  this  does 
not  always  hold  true.  Thus  if  we  say  that  "  a  good  book 
is  valued  either  for  the  usefulness  of  its  contents  or  the 
excellence  of  its  style,"  it  does  not  by  any  means  follow 
because  the  contents  of  a  book  are  useful  that  its  style  is 
not  excellent  We  generally  choose  alternatives  which 
are  inconsistent  with  each  other;  but  this  is  not  logically 
necessary. 

The  other  form  of  disjunctive  syllogism,  called  the 
modns  tolltndopentns  (the  mood  which  by  denying  affirms) , 
is  always  of  necessity  cogent,  and  is  as  follows : 

A  is  either  £  or  C, 

But  A  is  not  5; 

Therefore  A  is  C. 

Thus  if  we  suppose  a  book  to  be  valued  only  foe  the 
Mefulness  of  its  contents  or  the  excellence  of  its  style,  it 
follows  that  if  a  book  be  valued  but  not  for  the  former 
reason  it  must  be  for  the  latter ;  and  vice  versa.  If  th« 
time  of  yeax  be  not  spring,  it  must  be  summer,  autumn  w 


MX.]  ARGUMENTS.  I* 

winter ;  if  it  be  not  autumn  nor  winter,  it  must  be  eithe 
spring  or  summer;  and  so  on.  In  short  if  any  alternatives 
be  denied,  the  rest  remain  to  be  affirmed  as  before.  It 
will  be  noticed  that  the  disjunctive  syllogism  is  governed 
by  totally  different  rules  from  the  ordinary  categorical 
iyllogism,  since  a  negative  premise  gives  an  affirmative 
ronclusion  in  the  former,  and  a  negative  conclusion  in 
the  latter. 

There  yet  remains  a  form  of  argument  called  the 
Dilemma,  because  it  consists  in  assuming  two  alternatives, 
usually  called  the  horns  of  the  dilemma,  and  yet  proves 
something  in  either  case  (Greek  dt-  two ;  X^fio,  assump- 
tion). Mr  Mansel  defines  this  argument  as  "  a  syllogism, 
having  a  conditional  major  premise  with  more  than  one 
antecedent,  and  a  disjunctive  minor."  There  are  at  least 
three  forms  in  which  it  may  be  stated.  The  first  form  is 
called  the  Simple  Constructive  Dilemma : 

If  A  is  B,  C  is  D\  and  if  E  is  F,  C  is  D , 
But  either  A  is  By  or  E  is  F\ 
Therefore  C  is  D. 

Thus  "if  a  science  furnishes  useful  facts,  it  is  worthy  o 
being  cultivated;  and  if  the  study  of  it  exercises  the 
reasoning  powers,  it  is  worthy  of  being  cultivated;  but 
either  a  science  furnishes  useful  facts,  or  its  study 
exercises  the  reasoning  powers ;  therefore  it  is  worthy  ol 
being  cultivated." 

The  second  form  of  dilemma  is  the  Complex  Co* 
•tractive  Dilemma,  which  is  as  follows : 

If  A  is£,CisD;  and  if  E  is  F,  G  is  H\ 
But  either  A  is  B,  or  E  is  F\ 
Therefore  either  C  is  D,  or  G  is  H+ 

It  is  called  complex  because  the  conclusion  it  in  the 
disjunctive  form  As  an  instance  we  may  take  the  argi* 


id3  OF  CONDITIONAL  [Llcsi 

ment,  "  If  a  statesman  who  sees  his  former  opinions  tc 
be  wrong  does  not  alter  his  course  he  is  guilty  of  deceit ; 
and  if  he  does  alter  his  course  he  is  open  to  a  charge 
of  inconsistency ;  but  either  he  does  not  alter  his  course 
or  he  does ;  therefore  he  is  either  guilty  of  deceit,  or  he  is 
open  to  a  charge  of  inconsistency."  In  this  case  as  in 
the  greater  number  of  dilemmas  the  terms  A,B,C,  D,  &c. 
are  not  all  different. 

The  Destructive  Dilemma  is  always  complex,  because 
it  could  otherwise  be  resolved  into  two  unconnected  de- 
structive hypothetical  syllogisms.  It  is  in  the  following 
form: 

If  A  is  £,  Cis  D\  and  if  E  is  F,  G  is  H\ 
But  either  C  is  not  D,  or  G  is  not  H\ 
Therefore  either  A  is  not  Z?,  or  E  is  not  f. 

For  instance,  "  If  this  man  were  wise,  he  would  no 
speak  irreverently  of  Scripture  in  jest;  and  if  he  wert 
good,  he  would  not  do  so  in  earnest ;  but  he  does  it  either 
in  jest  or  earnest ;  therefore  he  is  either  not  wise,  or  not 
good*." 

Dilemmatic  arguments  are  however  more  often  fal- 
lacious than  not,  because  it  is  seldom  possible  to  find 
instances  where  two  alternatives  exhaust  all  the  possible 
cases,  unless  indeed  one  of  them  be  the  simple  negative 
of  the  other  in  accordance  with  the  law  of  excluded  mid- 
dle (p.  1 19).  Thus  if  we  were  to  argue  that  "  if  a  pupil  is 
fond  of  learning  he  needs  no  stimulus,  and  that  if  he  dis- 
likes learning  no  stimulus  will  be  of  any  avail,  but  as  he 
is  either  fond  of  learning  or  dislikes  it,  a  stimulus  is  eithex 
needless  or  of  no  avail,"  we  evidently  assume  improperly 
the  disjunctive  minor  premise.  Fondness  ,and  dislike  art 
tot  the  only  two  possible  alternatives,  fot  there  may  bf 

*  Whately. 


XIX.J  ARGUMENTS.  16 

some  irho  are  neither  fond  of  learning  nor  dislike  it,  an*, 
to  these  a  stimulus  in  the  shape  of  rewards  may  be  de- 
sirablr.  Almost  anything  can  be  proved  if  we  arc  allowed 
thus  to  pick  out  two  of  the  possible  alternatives  which  aw 
in  our  favour,  and  aigue  from  these  alone. 

A  dilemma  can  often  be  retorted  by  producing  a« 
cogent  a  dilemma  to  the  contrary  effect.  Thus  an  Athe- 
nian mother,  according  to  Aristotle,  addressed  her  son  in 
the  following  words  :  "Do  not  enter  into  public  business , 
for  if  you  say  what  is  just,  men  will  hate  you  ;  and  if  you 
say  what  is  unjust,  the  Gods  will  hate  you."  To  which 
Aristotle  suggests  the  following  retort :  "  I  ought  to  enter 
into  public  affairs  ;  for  if  I  say  what  is  just,  the  Gods  wu, 
love  me ;  and  if  I  say  what  is  unjust,  men  will  love  me." 

Mansel's  Aldrich,  App.  Note  I,  on  the  Hypothetic*. 
Syllogism, 


LESSON  XX. 

LOGICAL  FALLACIES. 

IN  order  to  acquire  a  satisfactory  knowledge  of  the  rule* 
of  correct  thinking,  it  is  essential  that  we  should  become 
acquainted  with  the  most  common  kinds  of  fallacy  ;  that 
is  to  say,  the  modes  in  which,  by  neglecting  the  rules  of 
logic,  we  often  fall  into  erroneous  reasoning.  In  previous 
lessons  we  have  considered,  as  it  were,  how  to  find  the 
right  road ;  it  is  our  task  here  to  ascertain  the  turnings  at 
which  we  are  most  liable  to  take  the  wrong  road. 

In  describing  the  fallacies  I  shall  follow  the  order  and 
adopt  the  mode  of  classification  which  has  been  usual 
for  the  last  2000  years  and  more,  since  in  fact  the  grei/ 


170  LOGICAL  FALLACIES.  [Lisa 

teacher  Aristotle  first  explained  the  fallacies.  According 
to  this  mode  of  arrangement  fallacies  are  divided  into  two 
principal  groups,  containing  the  logical  and  the  material 
fallacies. 

1.  The  logical  fallacies  are  those  which  occur  in  the 
toere  form  of  the  statement ;  or  as  it  is  said  in  the  old 
Latin  expressions,  in  dictione,  or  in  voce.    It  is  supposed 
accordingly  that  fallacies  of  this  kind  can  be  discovered 
without  a  knowledge  of  the  subject-matter  with  which  the 
argument  is  concerned 

2.  The  material  fallacies,  on  the  contrary,  arise  out- 
side of  the  mere  verbal  statement,  or  as  it  is  said,  eoctra 
dictionem;  they  are  concerned  consequently  with  the  sub- 
ject of  the  argument,  or  in  re  (in  the  matter),  and  cannot 
be  detected  and  set  right  but  by  those  acquainted  with 
the  subject. 

The  first  group  of  logical  fallacies  may  be  further  di- 
vided into  the  purely  logical  and  the  semi-logical^  and  we 
may  include  in  the  former  class  the  distinct  breaches  of 
the  syllogistic  rules  which  have  already  been  described. 
Thus  we  may  enumerate  as  Purely  Logical  Fallacies : 

1.  Fallacy  of  four  terms  (Quatemio  Terminorum) — 
Breach  of  Rule  i  ; 

2.  Fallacy  of  undistributed  middle — Breach  of  Rule  3  j 

3.  Fallacy  of  illicit  process,  of  the  major  or  minor 
term — Breach  of  Rule  4  ; 

4.  Fallacy  of  negative  premises — Breach  of  Rule  5  ; 
as  well  as  breaches  of  the  6th  rule,  to  which  no  distinct 
name  has  been  given.     Breaches  of  the  7th  and  8th  rules 
may  be  resolved  into  the  preceding  (p.  151),  but  they 
nay  also  be  described  as  in  p.  135. 

The  other  part  of  the  class  of  logical  fallacies  containi 
Bemi-logical  fallacies,  which  are  six  in  number,  as  follows 


UtJ  LOGICAL   FALLACIES.  Ifl 

1.  Fallacy  of  Equivocation. 

2.  Fallacy  of  Amphibology. 

3.  Fallacy  of  Composition. 

4.  Fallacy  of  Division. 

5.  Fallacy  of  Accent 

6.  Fallacy  of  Figure  of  Speech. 
These  t  jhall  describe  and  illustrate  in  succession 

Equivocation  consists  in  the  same  term  being  used 
in  two  distinct  senses  ;  any  of  the  three  terms  of  the  syl- 
logism may  be  subject  to  this  fallacy,  but  it  is  usually  the 
middle  term  which  is  used  in  one  sense  in  one  premise 
and  in  another  sense  in  the  other.  In  this  case  it  is  often 
called  the  fallacy  of  ambiguous  middle,  and  when  we  dis- 
tinguish the  two  meanings  by  using  other  suitable  modes 
of  expression  it  becomes  apparent  that  the  supposed  syl- 
logism contains  four  terms.  The  fallacy  of  equivocation 
may  accordingly  be  considered  a  disguised  fallacy  of  four 
terms.  Thus  ii  a  person  were  to  argue  that  "  all  criminal 
actions  ought  U»  be  punished  by  law;  prosecutions  for 
theft  are  crimiivil  actions;  therefore  prosecutions  for 
theft  ought  to  bt  punished  by  law,"  it  is  quite  apparent 
that  the  term  "criminal  action"  means  totally  different 
things  in  the  tw->  premises,  and  that  there  is  no  true 
middle  term  at  al  I.  Often,  however,  the  ambiguity  is  of 
a  subtle  and  difficult  character,  so  that  different  opinions 
may  be  held  conct  rning  it.  Thus  we  might  argue  : 

"He  who  hanns  another  should  be  punished.  He 
who  communicate*  an  infectious  disease  to  another  per- 
son harms  him.  Therefore  he  who  communicates  an 
infectious  disease  to  another  person  should  be  punished." 

This  may  or  may  not  be  held  to  be  a  correct  argument 
according  to  the  kinds  of  actions  we  should  consider  to 
come  under  the  term  harm,  according  as  we  regard  negli- 
gence or  malice  requisite  to  constitute  harm.  Mam 


172  LOGICAL  FALLACIES.  fLESS 

difficult  legal  questions  are  of  this  nature,  as  for 
stance: 

Nuisances  are  punishable  by  law  ; 

To  keep  a  noisy  dog  is  a  nuisance ; 

To  keep  a  noisy  dog  is  punishable  by  law. 

The  question  here  would  turn  upon  the  degree  oi 
auisance  which  the  law  would  interfere  to  prevent  Oi 
again  : 

Interference  with  another  man's  business  is  illegal; 
Underselling  interferes  with  another  man's  business; 
Therefore  underselling  is  illegal 

Here  the  question  turns  upon  the  kind  of  interference, 
and  it  is  obvious  that  underselling  is  not  the  kind  of  in- 
terference referred  to  in  the  major  premise. 

The  Fallacy  of  Amphibology  consists  in  an  ambiguous 
grammatical  structure  of  a  sentence,  which  produces  mis- 
conception. A  celebrated  instance  occurs  in  the  prophecy 
of  the  spirit  in  Shakspeare's  Henry  VI. :  "  The  Duke  yet 
lives  that  Henry  shall  depose,"  which  leaves  it  wholly 
doubtful  whether  the  Duke  shall  depose  Henry,  or  Henry 
the  Duke.  This  prophecy  is  doubtless  an  imitation  of 
those  which  the  ancient  oracle  of  Delphi  is  reported  to 
have  uttered ;  and  it  seems  that  this  fallacy  was  a  great 
resource  to  the  oracles  who  were  not  confident  in  their 
own  powers  of  foresight.  The  Latin  language  gives  great 
scope  to  misconstructions,  because  it  does  not  require 
any  fixed  order  for  the  words  of  a  sentence,  and  when 
there  are  two  accusative  cases  with  an  infinitive  verb,  it 
may  be  difficult  to  tell  except  from  the  context  which 
comes  in  regard  to  sense  before  the  verb.  The  double 
meaning  which  may  be  given  to  "twice  two  and  three" 
arises  from  amphibology ;  it  may  be  7  or  10,  according 
as  we  add  the  3  after  or  before  multiplying.  In  the 
careless  construction  of  sentences  it  is  often  impossible  to 


JOL]  LOGICAL  FALLACIES.  173 

tell  to  what  part  any  adverb  or  qualifying  clause  refers. 
Thus  if  a  person  says  "  I  accomplished  my  business  and 
returned  the  day  after,"  it  may  be  that  the  business  was 
accomplished  on  the  day  after  as  well  as  the  return  ;  but 
it  may  equally  have  been  finished  on  the  previous  day. 
Any  ambiguity  of  this  kind  may  generally  be  avoided  by 
a  simple  change  in  the  order  of  the  words;  as  for  instance, 
*  I  accomplished  my  business,  and,  on  the  day  after, 
returned."  Amphibology  may  sometimes  arise  from  con- 
fusing the  subjects  and  predicates  in  a  compound  sentence, 
as  if  in  "platinum  and  iron  are  very  rare  and  useful 
metals "  I  were  to  apply  the  predicate  useful  to  platinum 
and  rare  to  iron,  which  is  not  intended.  The  word  "  re- 
spectively" is  often  used  to  shew  that  the  reader  is  not  at 
liberty  to  apply  each  predicate  to  each  subject. 

The  Fallacy  of  Composition  is  a  special  case  of  equivo- 
cation, arising  from  the  confusion  of  an  universal  and  a 
collective  term.  In  the  premises  of  a  syllogism  we  may 
affirm  something  of  a  class  of  things  distributively^  that  is, 
of  each  and  any  separately,  and  then  we  may  in  the  con- 
clusion infer  the  same  of  the  whole  put  together.  Thus  we 
may  say  that  "  all  the  angles  of  a  triangle  are  less  than  two 
right  angles,"  meaning  that  any  of  the  angles  is  less  than 
two  right  angles ;  but  we  must  not  infer  that  all  the  angles 
put  together  are  less  than  two  right  angles.  We  must  not 
argue  that  because  every  member  of  a  jury  is  very  likely 
to  judge  erroneously,  the  jury  as  a  whole  are  also  ver> 
likely  to  judge  erroneously ;  nor  that  because  each  of  the 
witnesses  in  a  law  case  is  liable  to  give  false  or  mis- 
taken evidence,  no  confidence  can  be  reposed  in  the  con- 
current testimony  of  a  number  of  witnesses.  It  is  by  a 
fallacy  of  Composition  that  protective  duties  are  still 
sometimes  upheld.  Because  any  one  or  any  few  trades 
which  enjoy  protective  duties  are  benefited  thereby,  it  u 
supposed  that  all  trades  at  once  might  be  benefited  simi 


174  LOGICAL  FALLACIES.  [LES& 

larly ;  but  this  is  impossible,  because  the  protection  of  one 
trade  by  raising  prices  injures  all  others. 

The  Fallacy  of  Division  is  the  converse  of  the  pre- 
ceding, and  consists  in  using  the  middle  term  col- 
lectively in  the  major  premise  but  distributively  in  th« 
minor,  so  that  the  whole  is  divided  into  its  parts.  Thus 
it  might  be  argued,  "All  the  angles  of  a  triangle  are 
'together)  equal  to  two  right  angles;  ABC  is  an  angle  of 
a  triangle ;  therefore  ABC  is  equal  to  two  right  angles." 
Or  again,  "  The  inhabitants  of  the  town  consist  of  men, 
women  and  children  of  all  ages ;  those  who  met  in  the 
Guildhall  were  inhabitants  of  the  town;  therefore  they 
consisted  of  men,  women  and  children  of  all  ages;"  or, 
"  The  judges  of  the  court  of  appeal  cannot  misinterpret 
the  law;  Lord  A.B.  is  a  judge  of  the  court  of  appeal; 
therefore  he  cannot  misinterpret  the  law." 

The  Fallacy  of  Accent  consists  in  any  ambiguity 
arising  from  a  misplaced  accent  or  emphasis  thrown  upon 
some  word  of  a  sentence.  A  ludicrous  instance  is  liable 
to  occur  in  reading  chapter  xiii.  of  the  First  Book  of 
Kings,  verse  27,  where  it  is  said  of  the  prophet  "And  he 
spake  to  his  sons,  saying,  Saddle  me  the  ass.  And  they 
saddled  him."  The  italics  indicate  that  the  word  him 
was  supplied  by  the  translators  of  the  authorized  version, 
but  it  may  suggest  a  very  different  meaning.  The  Com- 
mandment "Thou  shalt  not  bear  false  witness  against 
thy  neighbour  "  may  be  made  by  a  slight  emphasis  of  the 
voice  on  the  last  word  to  imply  that  we  are  at  liberty  to 
bear  false  witness  against  other  persons.  Mr  De  Morgan 
who  remarks  this  also  points  out  that  the  erroneous 
quoting  of  an  author,  by  unfairly  separating  a  word  from 
its  context  or  italicising  words  which  were  not  intended 
to  be  italicised,  gives  rise  to  cases  of  this  fallacy. 

It  is  curious  to  observe  how  many  and  various  may  be 
the  meanings  attributable  to  the  same  sentence  according 


«.]  LOGICAL  FALLACIES.  17$ 

as  emphasis  is  thrown  upon  one  word  or  another.  Thui 
the  sentence  "The  study  of  Logic  is  not  supposed  tt 
communicate  a  knowledge  of  many  useful  facts,"  may  b« 
made  to  imply  that  the  study  of  Logic  does  communicate 
such  a  knowledge  although  it  is  not  supposed  to ;  or  that 
it  communicates  a  knowledge  of  a  few  useful  facts ;  or 
that  it  communicates  a  knowledge  of  many  useless  facts. 
This  ambiguity  may  be  explained  by  considering  that  if 
you  deny  a  thing  to  have  the  group  of  qualities  Ay  B,  C,  D, 
the  truth  of  your  statement  will  be  satisfied  by  any  one 
quality  being  absent,  and  an  accented  pronunciation  will 
often  be  used  to  indicate  that  which  the  speaker  believes 
to  be  absent.  If  you  deny  that  a  particular  fruit  is  ripe 
and  sweet  and  well-flavoured,  it  may  be  unripe  and  sweet 
and  well-flavoured;  or  ripe  and  sour  and  well-flavour- 
ed; or  ripe  and  sweet  and  ill-flavoured;  or  any  two  or 
even  all  three  qualities  may  be  absent.  But  if  you  deny 
it  to  be  ripe  and  sweet  and  well-flavoured,  the  denial 
would  be  understood  to  refer  to  the  last  quality.  Jeremy 
Bentham  was  so  much  afraid  of  being  misled  by  this 
fallacy  of  accent  that  he  employed  a  person  to  read  to 
him,  as  I  have  heard,  who  had  a  peculiarly  monotonous 
manner  of  reading. 

The  Fallacy  of  the  Figure  of  Speech  is  the  sixth  and 
last  of  the  semi-logical  fallacies,  and  is  of  a  very  trifling 
character.  It  appears  to  consist  in  any  grammatical 
mistake  or  confusion  between  one  part  of  speech  and  an- 
other. Aristotle  gravely  gives  the  following  instance : 
"  Whatever  a  man  walks  he  tramples  on ;  a  man  walki 
the  whole  day ;  therefore  he  tramples  on  the  day."  Heft 
•n  adverbial  phrase  is  converted  into  a  noun  object 


LESSON  XXL 

MATERIAL  FALLACIES. 

THE  Material  fallacies  are  next  to  be  considered;  and  thefc. 
importance  is  very  great,  although  it  is  not  easy  tfl 
illustrate  them  by  brief  examples.  There  are  altogethet 
seven  kinds  of  such  fallacies  enumerated  by  Aristotle  and 
adopted  by  subsequent  logicians,  as  follows  : 

1.  The  Fallacy  of  Accident 

2.  The  Converse  Fallacy  of  Accident. 

3.  The  Irrelevant  Conclusion. 

4.  The  Petitio  Principii. 

5.  The  Fallacy  of  the  Consequent  or  Non  seqnitor. 

6.  The  False  Cause. 

7.  The  Fallacy  of  Many  Questions. 

Of  these  the  two  first  are  conveniently  described  to- 
gether. The  fallacy  of  accident  consists  in  arguing  erro- 
neously from  a  general  rule  to  a  special  case,  where  a 
certain  accidental  circumstance  renders  the  rule  inappli- 
cable. The  converse  fallacy  consists  in  arguing  from  a 
special  case  to  a  general  one.  This  latter  fallacy  is  usu- 
ally described  by  the  Latin  phrase  a  ditto  secundum  quid 
ad  dictum  simpliciter,  meaning  "  from  a  statement  undei 
a  condition  to  a  statement  simply  or  without  that  con- 
dition." Mr  De  Morgan  has  remarked  in  his  very  inte* 
resting  Chapter  on  Fallacies*  that  we  ought  to  add  a 
third  fallacy,  which  would  consist  in  arguing  from  om 
tpecial  case  to  another  special  case. 

*  formal  Lo&,  Chapter  XIIL 


LESS,  xxi.]    MATERIAL  FALLACIES.  177 

I  will  try  by  a  few  examples  to  illustrate  these  kinds  of 
fallacy,  but  much  difficulty  is  often  encountered  in  saying 
to  which  of  the  three  any  particular  example  is  best  r* 
ferred.  A  most  ancient  example  repeated  in  almost  every 
logical  hand-book  is  as  follows  :  "  What  you  bought  yes 
terday  you  eat  to-day  ;  you  bought  raw  meat  yesterday; 
therefore  you  eat  raw  meat  to-day."  The  assertion  in  the 
conclusion  is  made  of  meat  with  the  accidental  quality  of 
rawness  added,  where  the  first  premise  evidently  speaks  oi 
the  substance  of  the  meat  without  regard  to  its  accidental 
condition.  This  then  is  a  case  of  the  direct  fallacy. 
If  it  is  argued  again  that  because  wine  acts  as  a  poison 
when  used  in  excess  it  is  always  a  poison,  we  fall  into  the 
converse  fallacy. 

It  would  be  a  case  of  the  direct  fallacy  of  accident 
to  infer  that  a  magistrate  is  justified  in  using  his  power 
to  forward  his  own  religious  views,  because  every  man 
has  a  right  to  inculcate  his  own  opinions.  Evidently 
a  magistrate  as  a  man  has  the  rights  of  other  men,  but 
in  his  capacity  of  a  magistrate  he  is  distinguished  from 
other  men,  and  he  must  not  infer  of  his  special  powers 
in  this  respect  what  is  only  true  of  his  rights  as  a 
man.  For  another  instance  take  the  following  :  "  He  who 
thrusts  a  knife  into  another  person  should  be  punished ; 
a  surgeon  in  operating  does  so;  therefore  he  should  be 
ounished."  Though  the  fallacy  of  this  is  absurdly 
manifest,  it  is  not  so  manifest  how  we  are  to  classify  the 
error.  We  may  for  instance  say  that  as  a  general  rule 
whoever  stabs  or  cuts  another  is  to  be  punished  unless  it 
can  be  snewn  to  have  been  done  under  exceptional  cir- 
cumstances, as  by  a  duly  qualified  surgeon  acting  for  the 
i?ood  of  the  person.  In  this  case  the  example  belongs  to 
the  direct  fallacy  of  accident.  In  another  view  we  might 
interpret  the  first  premise  to  mean  the  special  case  of 
thrusting  a  knife  maliciously;  to  argue  from  that  to  thf 

12 


178  MATERIAL  FALLACIES.  [L 

case  of  a  surgeon  would  be  to  infer  from  one  special  CAM 
to  another  special  case. 

It  is  undoubtedly  true  that  to  give  to  beggars  promote! 
mendicancy  and  causes  evil ;  but  if  we  interpret  this  tc 
mean  that  assistance  is  never  to  be  given  to  those  whc 
solicit  it,  we  fall  into  the  converse  fallacy  of  accident, 
inferring  of  all  who  solicit  alms  what  is  only  true  of  those 
who  solicit  alms  as  a  profession.  Similarly  it  is  a  very 
good  rule  to  avoid  lawsuits  and  quarrels,  but  only  as  a 
general  rule,  since  there  frequently  arise  circumstances 
in  which  resort  to  the  law  is  a  plain  duty.  Almost  all 
the  difficulties  which  we  meet  in  matters  of  law  ana 
moral  duty  arise  from  the  impossibility  of  always  ascer- 
taining exactly  to  what  cases  a  legal  or  moral  rule  does 
or  does  not  extend  ;  hence  the  interminable  differences 
of  opinion,  even  among  the  judges  of  the  land. 

The  Third  Material  Fallacy  is  that  of  the  Irrelevant 
Conclusion,  technically  called  the  Ignoratio  EUnchi,  or 
literally  Ignorance  of  the  Refutation.  It  consists  in 
arguing  to  the  wrong  point,  or  proving  one  thing  in  such 
a  manner  that  it  is  supposed  to  be  something  else  that  is 
proved.  Here  again  it  would  be  difficult  to  adduce  con- 
cise examples,  because  the  fallacy  usually  occurs  in  the 
course  of  long  harangues,  where  the  multitude  of  words 
and  figures  leaves  room  for  confusion  of  thought  and 
forgetfulness.  This  fallacy  is  in  fact  the  great  resource  of 
those  who  have  to  support  a  weak  case.  It  is  not  un- 
known in  the  legal  profession,  and  an  attorney  for  the 
defendant  in  a  lawsuit  is  said  to  have  handed  to 
the  barrister  his  brief  marked,  "No  case ;  abuse  the 
plaintiffs  attorney."  Whoever  thus  uses  what  is  known  as 
trgumentum  ad  homintm,  that  is  an  argument  which 
rests,  not  upon  the  merit  of  the  case,  but  the  character  or 
position  of  those  engaged  in  it,  commits  this  fallacy.  II 
a  man  is  accused  of  a  crime  it  is  no  answer  to  say  thai 


KXL]  MATERIAL  FALLACIES.  ift 

the  prosecutor  is  as  bad.  If  a  great  change  in  the  law  is 
proposed  in  Parliament,  it  is  an  Irrelevant  Conclusion  tc 
argue  that  the  proposer  is  not  the  right  man  to  bring  it 
forward.  Everyone  who  gives  advice  lays  himself  open 
to  the  retort  that  he  who  preaches  ought  to  practise,  or 
that  those  who  live  in  glass  houses  ought  not  to  throw 
stones.  Nevertheless  there  is  no  necessary  connection 
between  the  character  of  the  person  giving  advice  and 
the  goodness  of  the  advice. 

The  argumentum  ad  populum  is  another  form  01 
Irrelevant  Conclusion,  and  consists  in  addressing  argu- 
ments to  a  body  of  people  calculated  to  excite  their  feel- 
ings and  prevent  them  from  forming  a  dispassionate 
judgment  upon  the  matter  in  hand.  It  is  the  great 
weapon  of  rhetoricians  and  demagogues. 

Petitlo  Principil  is  a  familiar  name,  and  the  nature  of 
the  fallacy  it  denotes  is  precisely  expressed  in  the  phrase 
begging  the  question.  Another  apt  name  for  the  fallacy  is 
circulus  inprobando,  or  "a  circle  in  the  proof."  It  con- 
sists in  taking  the  conclusion  itself  as  one  of  the  premises 
of  an  argument  Of  course  the  conclusion  of  a  syllogism 
must  always  be  contained  or  implied  in  the  premises,  but 
only  when  those  premises  are  combined,  and  are  dis- 
tinctly different  assertions  from  the  conclusion.  Thus  in 
the  syllogism, 

Bi*C, 
AkB, 

therefore  A  is  C, 

the  conclusion  is  proved  by  being  deduced  from  two 
propositions,  neither  of  which  is  identical  with  it  ;  but  if 
the  truth  of  one  of  these  premises  itself  depends  upott 
.he  following  syllogism, 


AisC, 
therefore  A  is  Bt 

12—  * 


tdo  MATERIAL  FALLACIES.  [Uta 

it  is  plain  that  we  attempt  to  prove  a  proposition  by  itself 
which  is  as  reasonable  as  attempting  to  support  a  body 
upon  itself.  It  is  not  easy  to  illustrate  this  kind  of  fal- 
lacy by  examples,  because  it  usually  occurs  in  long  argu- 
ments, and  especially  in  wordy  metaphysical  writings 
We  are  very  likely  to  fall  into  it  however  when  we  employ 
a  mixture  of  Saxon  and  Latin  or  Greek  words,  so  as  to 
appear  to  prove  one  proposition  by  another  which  is 
really  the  same  expressed  in  different  terms,  as  in  the 
following:  "Consciousness  must  be  immediate  cognition 
of  an  object ;  for  I  cannot  be  said  really  to  know  a  thing 
unless  my  mind  has  been  affected  by  the  thing  itself." 

In  the  use  of  the  disjunctive  syllogism  this  fallacy  is 
likely  to  happen  ;  for  by  enumerating  only  those  alterna- 
tives which  favour  one  view  and  forgetting  the  others  it  is 
easy  to  prove  anything.  An  instance  of  this  occurs  in  the 
celebrated  sophism  by  which  some  of  the  ancient  Greek 
philosophers  proved  that  motion  was  impossible.  For, 
said  they,  a  moving  body  must  move  either  in  the  place 
where  it  is  or  the  place  where  it  is  not ;  now  it  is  absurd 
that  a  body  can  be  where  it  is  not,  and  if  it  moves  it  can- 
not be  in  the  place  where  it  is;  therefore  it  cannot  move 
at  alL  The  error  arises  in  the  assumption  of  a  premise 
which  begs  the  question;  the  fact  of  course  is  that  the 
body  moves  between  the  place  where  it  is  at  one  moment 
and  the  place  where  it  is  at  the  next  moment. 

Jeremy  Bentham  however  pointed  out  that  the  use 
even  of  a  single  name  may  imply  a  Petitio  Principii. 
Thus  in  a  Church  assembly  or  synod,  where  a  discussion 
is  taking  place  as  to  whether  a  certain  doctrine  should  be 
condemned,  it  would  be  a  Petitio  Principii  to  argue  thai 
the  doctrine  is  heresy,  and  therefore  it  ought  to  be  con- 
demned. To  assert  that  it  is  heresy  is  to  beg  the  question, 
because  every  one  understands  by  heresy  a  doctrine 
which  is  to  be  condemned.  Similarly  in  Parliament  • 


XXL]  MATERIAL  FALLACIES.  iSi 

bill  is  often  opposed  on  the  ground  that  it  is  unconstitu- 
tional and  therefore  ought  to  be  rejected;  but  as  no 
precise  definition  can  be  given  of  what  is  or  is  not  con- 
stitutional, it  means  little  more  than  that  the  measure  is 
distasteful  to  the  opponent.  Names  which  are  used  in 
this  fallacious  manner  were  aptly  called  by  Bentham 
Question-begging  Epithets.  In  like  manner  we  beg  the 
question  when  we  oppose  any  change  by  saying  that  it  is 
un-English. 

The  Fallacy  of  the  Consequent  is  better  understood 
by  the  familiar  phrase  non  sequitur.  We  may  apply 
this  name  to  any  argument  which  is  of  so  loose  and 
inconsequent  a  character  that  no  one  can  discover  any 
cogency  in  it.  It  thus  amounts  to  little  more  than  the 
Assertion  of  a  conclusion  which  has  no  connection  with 
the  premises.  Prof.  De  Morgan  gives  as  an  example 
the  following :  "  Episcopacy  is  of  Scripture  origin ;  the 
Church  of  England  is  the  only  episcopal  Church  in  Eng- 
land; ergo,  the  Church  established  is  the  Church  that 
should  be  supported." 

By  the  Fallacy  of  the  False  Cause  I  denote  that  which 
has  generally  been  referred  to  by  the  Latin  phrase  mm 
causa  pro  causd.  In  this  fallacy  we  assume  that  one 
thing  is  the  cause  of  another  without  any  sufficient 
grounds.  A  change  in  the  weather  is  even  yet  attributed 
to  the  new  moon  or  full  moon  which  had  occurred  shortly 
before,  although  it  has  been  demonstrated  over  and  over 
again  that  the  moon  can  have  no  such  effect.  In  former 
centuries  any  plague  or  other  public  calamity  which  fol- 
lowed the  appearance  of  a  comet  or  an  eclipse  was 
considered  to  be  the  result  of  it  The  Latin  phrase  post 
ko^  ergo  propter  hoc  (after  this  and  therefore  in  conse- 
quence of  this)  exactly  describes  the  character  of  these 
fallacious  conclusions.  Though  we  no  longer  dread  signs 
and  omens,  yet  we  often  enough  commit  the  fallacy;  as 


1 82  MATERIAL   FALLACIES.    [LESS.  XXL 

when  we  assume  that  all  the  prosperity  of  England  is  the 
result  of  the  national  character,  forgetting  that  the  plenti- 
ful coal  in  the  country  and  its  maritime  position  have 
contributed  to  our  material  wealth.  It  is  no  doubt  equally 
fallacious  to  attribute  no  importance  to  national  character; 
and  to  argue  that  because  England  has  in  past  centuries 
misgoverned  Ireland  all  the  present  evils  of  Ireland  art 
due  to  that  misgovernment 

Lastly  there  is  the  somewhat  trivial  Fallacy  of  Manj 
Questions,  which  is  committed  by  those  who  so  combine 
two  or  three  questions  into  one  that  no  true  answer  can 
be  given  to  them.  I  cannot  think  of  a  better  example 
than  the  vulgar  pleasantry  of  asking,  "  Have  you  left  ofl 
beating  your  mother?"  Questions  equally  as  unfair  are 
constantly  asked  by  barristers  examining  witnesses  in  a 
court  of  justice,  and  no  one  can  properly  be  required  to 
answer  Yes  or  No  to  every  question  which  may  be  ad- 
dressed to  him.  As  Aristotle  says,  "  Several  questions 
put  as  one  should  be  at  once  decomposed  into  theii 
several  parts.  Only  a  single  question  admits  of  a  single 
answer :  so  that  neither  several  predicates  of  one  subject 
nor  one  predicate  of  several  subjects,  but  only  one  predi- 
cate of  one  subject,  ought  to  be  affirmed  or  denied  ir  a 
tingle  answer." 

Read  Prof,  de  Morgan's  excellent  and  amusing  Chaptei 

on  Fallacies,  Formal  Logic,  Ch.  XHL 
iVhately's  remarks  on  Fallacies,  Elements 

Book  IIL,  are  often  very  original  anc*  acute. 


LESSON   XXII. 
THE  QUANTIFICATION  OF  THE  PREDICATE 

THE  syllogism  has  been  explained  in  the  preceding  three 
lessons  almost  exactly  in  the  form  in  which  it  has  been 
taught  for  more  than  two  thousand  years.  Just  as  Geo- 
metry has  been  taught  in  the  way  and  order  first  adopted 
by  the  ancient  Greek  writer  Euclid,  so  Logic  has  been 
taught  nearly  as  Aristotle  taught  it  about  the  year  335  B.C. 

But  within  the  last  few  years  teachers  have  at  last 
come  to  the  conclusion  in  England  that  Euclid's  ideas  of 
Geometry  are  not  as  perfect  as  could  be  desired.  During 
the  last  30  or  40  years  also  it  has  been  gradually  made 
apparent  that  Aristotle's  syllogism  is  not  an  absolutely 
perfect  system  of  logical  deduction.  In  fact,  certain 
eminent  writers,  especially  Sir  William  Hamilton,  Pro- 
fessor De  Morgan,  Archbishop  Thomson  and  Dr  Boole, 
have  shewn  that  we  need  to  make  improvements  from  the 
very  basis  of  the  science. 

This  reform  in  Logic  is  called  by  the  somewhat  mys- 
terious name  of  the  quantification  of  the  predicate,  but 
the  reader  who  has  found  no  insuperable  difficulty  io 
the  preceding  lessons  need  not  fear  one  here.  To  quan- 
tify the  predicate  is  simply  to  state  whether  the  ivhoU  of 
tkt  part  only  of  the  predicate  agrees  t*ith  or  differ*  from 
the  subject.  In  this  proposition, 

«  All  metals  are  elements, " 


i«4  THE  QUANTIFICATION  [LESS 

the  subject  is  quantified,  but  the  predicate  is  not;  we 
know  that  all  metals  are  elements,  but  the  proposition 
does  not  distinctly  assert  whether  metals  make  the  whole 
of  the  elements  or  not.  In  the  quantified  proposition 

"  All  metals  are  some  elements," 

the  little  word  some  expresses  clearly  that  in  reality  the 
metals  form  only  a  part  of  the  elements.  Aristotle  avoid- 
ed the  use  of  any  mark  of  quantity  by  assuming,  as  we 
have  seen,  that  all  affirmative  propositions  have  a  par- 
ticular predicate,  like  the  example  just  given ;  and  that 
only  negative  propositions  have  a  distributed  or  universal 
predicate.  The  fact  however  is  that  he  was  entirely  in 
error,  and  thus  excluded  from  his  system  an  infinite 
number  of  affirmative  propositions  which  are  universal 
in  both  terms.  It  is  true  that — 

"All  equilateral  triangles  are  all  equiangular  triangles," 
but  this  proposition  could  not  have  appeared  in  his  system 
except  in  the  mutilated  form — 

"All  equilateral  triangles  are  equiangular." 
Such  a  proposition  as 

"London  is  the  capital  of  England," 
or  "  Iron  is  the  cheapest  metal," 

had  no  proper  place  whatever  in  his  syllogism,  since  both 
terms  aie  singular  and  identical  with  each  other,  and 
both  are  accordingly  universal. 

As  soon  as  we  allow  the  quantity  of  the  predicate  to 
De  stated  the  forms  of  reasoning  become  much  simplified. 
We  may  first  consider  the  process  of  conversion.  In  our 
lesson  on  the  subject  it  was  necessary  to  distinguish  be- 
tween conversion  by  limitation  and  simple  conversion. 
But  now  one  single  process  of  simple  conversion  is  suffi« 
cient  for  all  kinds  of  propositions.  Thus  the  quantified 
proposition  of  the  form  A, 

"All  metals  are  some  elements," 


XXIL]  OF  THE  PREDICATE.  18$ 

is  simply  converted  into 

"  Some  elements  are  all  metals,  * 
The  particular  affirmative  proposition 

"  Some  metals  are  some  brittle  substances  * 
becomes  by  mere  transposition  of  terms 

"  Some  brittle  substances  are  some  metals." 
rhe  particular  negative  proposition 

"  Some  men  are  not  (any)  trustworthy  persons11 
is  also  converted  simply  into 

"  Not  any  trustworthy  persons  are  some  men," 
though  the  result  may  appear  less  satisfactory  in  this  form 
than  in  the  affirmative  form,  as  follows, 

"  Some  men  are  some  not-trustworthy  persons," 
converted  simply  into 

"  Some  not -trustworthy  persons  are  some  men." 
The  universal  negative    proposition  2  is   converted 
simply  as  before,  and  finally  we  have  a  new  affirmative 
proposition  universal  both  in  subject  and  predicate  ;  as  in 
"All  equilateral  triangles  are  all  equiangular  triangles," 
which  may  obviously  be  converted  simply  into 
"All  equiangular  triangles  are  all  equilateral  triangles." 

This  doubly  universal  affirmative  proposition  is  of 
most  frequent  occurrence;  as  in  the  case  of  all  definitions 
and  singular  propositions ;  I  may  give  as  instances 
"Honesty  is  the  best  policy,"  "The  greatest  truths  are 
the  simplest  truths,"  "Virtue  alone  is  happiness  below," 
"  Self-exaltation  is  the  fool's  paradise." 

When  affirmative  propositions  are  expressed  in  the 
quantified  form  all  immediate  inferences  can  be  readily 
drawn  from  them  by  this  one  rule,  that  whatever  we  do 
with  one  term  we  should  do  with  the  other  term.  Thus 
from  the  doubly  universal  proposition,  "  Honesty  is  the 
best  policy,"  we  infer  that  "what  is  not  the  best  policy  is 


1 86  THE  QUANTIFICATION  [LESS 

not  honesty,"  and  also  "  what  is  not  honesty  is  not  the  best 
policy."  From  this  proposition  in  fact  we  can  draw  two 
contraposltlves  ;  but  the  reader  will  carefully  rememba 
that  from  the  ordinary  unquantified  proposition  A  we 
can  only  draw  one  contrapositive  (see  p.  84).  Thus  U 
"metals  arc  elements"  we  must  not  say  that  "what  are 
not  metals  are  not  elements."  But  if  we  quantify  the 
predicate  thus,  "All  metals  are  some  elements,"  we  may 
infer  that  "  what  are  not  metals  are  not  some  elements." 
Immediate  inference  by  added  determinant  and  complex 
conception  can  also  be  applied  in  either  direction  to 
quantified  propositions  without  fear  of  the  errors  noticed 
in  pp.  86-7. 

It  is  clear  that  in  admitting  the  mark  of  quantity  before 
the  predicate  we  shall  double  the  number  of  propositions 
which  must  be  admitted  into  the  syllogism,  because  the 
predicate  of  each  of  the  four  propositions  A,  E,  I,  0  may 
be  either  universal  or  particular.  Thus  we  arrive  at  a  list 
of  eight  conceivable  kinds  of  propositions,  which  are 
stated  in  the  following  table. 

U  All  X  is  all  Y.  j 

I  Some  X  is  some  K  I      Affirmative 

A  All  A"  is  some  K.  |     propositions. 

Y  Some  X  is  all  K 

E  No  X  is  (any)  Y.  ) 

•  Some  X  is  not  some  Y.  I    Negative 

1  No  X  is  some  K  |  propositions. 

0  Some  X  is  no  Y. 

The  letters  X  and  Y  are  used  to  stand  for  any  subject 
uid  predicate  respectively,  and  the  reader  by  substituting 
various  terms  can  easily  make  propositions  of  each  kind. 
The  symbolic  letters  on  the  left-hand  side  were  proposed 
by  Archbishop  Thomson  as  a  convenient  mode  of  reter 


XXIL]  OF  THE  PREDICATE.  ife 

ring  to  each  of  the  eight  propositions,  and  are  ver> 
suitably  chosen.  The  doubly  universal  affirmative  pro- 
position is  called  U ;  the  simple  converse  of  A  is  called 
f ;  the  Greek  letter  i\  (Eta,  e)  is  applied  to  the  proposi- 
tion obtained  by  changing  the  universal  predicate  of  I 
into  a  particular  predicate ;  and  the  Greek  «  (Omega,  d) 
is  applied  to  the  proposition  similarly  determined  from  0, 
All  these  eight  propositions  are  employed  by  Sir  W.  Ha- 
milton, but  Archbishop  Thomson  considers  that  two  of 
them,  n  and  •»,  are  never  really  used.  It  is  remarkable 
that  a  complete  table  of  the  above  eight  propositions  was 
given  by  Mr  George  Bentham  in  a  work  called  Outline 
of  a  New  System  of  Logic,  published  in  1827,  several 
years  previous  to  the  earliest  of  the  logical  publications  of 
3ir  W.  Hamilton.  But  Mr  Bentham  considered  that  some 
rf  the  propositions  are  hardly  to  be  distinguished  from 
others;  as  T  from  A,  of  which  it  is  the  simple  converse;  or 
ij  from  0. 

The  employment  even  of  the  additional  two  proposi- 
tions U  and  Y  introduced  by  Thomson  much  extends 
the  list  of  possible  syllogisms,  making  them  altogether  62 
in  number,  without  counting  the  fourth  figure,  which  is 
not  employed  by  Hamilton  and  Thomson.  When  the 
whole  eight  propositions  are  admitted  into  use  we  are 
obliged  to  extend  the  list  of  possible  syllogisms  so  as  to 
contain  12  affirmative  and  24  negative  moods  in  each  of 
the  three  first  figures.  The  whole  of  these  moods  are 
conveniently  stated  in  the  table  on.the  next  page,  given  by 
Archbishop  Thomson  at  p.  188  of  his  Laws  of  Thought. 

Sir  W.  Hamilton  also  devised  a  curious  system  of 
notation  for  exhibiting  all  the  moods  of  the  syllogism  in  a 
dear  manner.  He  always  employed  the  letter  M  to  denote 
the  middle  term  of  the  syllogism,  and  the  two  letters  C 
and  F  (the  Greek  capital  letter  Gamma)  for  the  two 
terms  appearing  in  the  conclusion.  The  copula  of  th« 


THE  QUANTIFICATION  \\XSL 

TaMe  of  Moods  of  Ou  Syllogism. 


FIRST  FIGURE. 

SECOND  Fio. 

THIRD  FIOUR*. 

Aftnn, 

Neg. 

Affirm.  ,    Neg. 

Affirm. 

Nef. 

1 

UUU 

EUE 

UUU  EUE 

UUU 

EUE 

UEE 

UEE 

UEF 

ti 

AYI 

,Y  » 

YYI 

OY« 

AAI 

7A» 

A0« 

YO- 

A,* 

iii 

AAA 

,A, 

YAA     OA, 

AYA 

A,, 

Y,  , 

AO*, 

iv 

YYY 

OYO 

AYY    ,YO 

YAY 

OAO 

YOO 

AOO 

Y,0 

V 

All 

,I« 

YII 

Gin 

All 

,1. 

* 

IYI 

«Y! 

IYI 

IY! 

IAI 

^A! 

Til 

UYY 

EYO 

UYY 

EYO 

UAY 

EAO 

UOO 

UOO 

u,o 

riii 

AUA 

,u, 

YUA    OU, 

AUA 

,u, 

AE, 

YE, 

AE, 

ix 

UAA 

EAE 

UAA 

EAE 

UYA 

EYE 

u,, 

u,, 

UOi? 

X 

YUY 

ouo 

AUY 

,UO 

YUY 

OUO 

YEE 

AEE 

YEE 

xi 

UII 

EIO 

UII 

EIO 

UII 

EIO 

xii 

IUI 

Tul 

IUI 

Tul 

IUI 

Tul 

IE,  I 

IE, 

IE, 

proposition  was  indicated  by  a  line  thickened  towards 
the  subject ;  thus  C  BB»_— —  M  means  that  "  Cis  M.* 
To  indicate  the  quantity  of  the  terms  Hamilton  inserted  a 


ttHl/1  OF  THE  PREDICATE.  189 

colon  (:)  between  the  term  and  the  copula  when  the 
quantity  is  universal,  and  a  comma  (,)  when  the  quantity 
is  particular.  Thus  we  readily  express  the  following 
affirmative  propositions. 

C  :  m  ,M    All  Cs  are  some  JTs       (A) 

C  :  mm\  :M    All  C's  are  all  J/'s  (V) 

C  ,  •«  ,  M    Some  C's  are  some  J/'s    (I) 

and  so  on.  Any  affirmative  proposition  can  be  converted 
into  the  corresponding  negative  proposition  by  drawing  a 
stroke  through  the  line  denoting  the  copula,  as  in  the 
following — 

C  :  •MM+-— —  '-M    No  C  is  any  M  (M) 

C ,  •w+— — -  :  M    Some  C  is  not  any  M      (0) 
C ,  •MM^— —  ,  M    Some  (7  is  not  some  M    («•) 

Any  syllogism  can  be  represented  by  placing  M  the 
middle  term  in  the  centre  and  connecting  it  on  each  side 
with  the  other  terms.  The  copula  representing  the  con- 
clusion can  then  be  placed  below;  Barbara  is  expressed 
as  follows — 


Tke  negative  mood  Celarent  is  similarly— 
Genre  in  the  second  figure  is  thus  represented-— 


Sir  W.  Hamilton  also  proposed  a  new  law  or  uprenw 
Anon  of  the  syllogism  by  which  the  validity  of  an!  forms 


190  THE  QUANTIFICATION  [LESS, 

of  the  syllogism  might  be  tested.  This  was  stated  in  tht 
following  words  :  "What  worse  relation  of  subject  and 
predicate  subsists  between  either  of  two  terms  and  a 
common  third  term,  with  which  both  are  related,  and  one 
at  least  positively  so — that  relation  subsists  between  these 
two  terms  themselves." 

By  a  worse  relation,  Sir  William  means  that  a  negative 
relation  is  worse  than  an  affirmative  and  a  particular  than 
a  universal.  This  canon  thus  expresses  the  rules  that  if 
there  be  a  negative  premise  the  conclusion  must  be  nega- 
tive, and  if  there  be  a  particular  premise  the  conclusion 
must  be  particular.  Special  canons  were  also  developed 
for  each  of  the  three  figures,  but  in  thus  rendering  the 
system  complex  the  advantages  of  the  quantified  form  of 
proposition  seem  to  be  lost. 

Prof.  De  Morgan  also  discovered  the  advantages  of 
the  quantified  predicate,  and  invented  a  system  differing 
greatly  from  that  of  Sir  W.  Hamilton.  It  is  fully  ex- 
plained in  his  Formal  Logic,  The  Syllabus  of  a  new 
System  of  Logic,  and  various  important  memoirs  on  the 
Syllogism  in  the  Transactions  of  the  Cambridge  Philo- 
sophical Society.  In  these  works  is  also  given  a  com- 
plete explanation  of  the  "  Numerically  Definite  Syllogism." 
Mr  De  Morgan  pointed  out  that  two  particular  premises 
may  often  give  a  valid  conclusion  provided  that  the 
actual  quantities  of  the  two  terms  are  stated,  and  when 
added  together  exceed  the  quantity  of  the  middle  term. 
Thus  if  the  majority  of  a  public  meeting  vote  for  the  first 
resolution,  and  a  majority  also  vote  for  the  second,  it 
follows  necessarily  that  some  who  voted  for  the  first  voted 
also  for  the  second.  The  two  majorities  added  togethei 
exceed  the  whole  number  of  the  meeting,  so  that  they 
could  not  consist  of  entirely  different  people.  They  may 
indeed  consist  of  exactly  the  same  people ;  but  all  that 
we  can  deduce  from  the  premises  is  that  the  excess  of  the 


xxil.]  OF  THE  PREDICATE.  19* 

two  majorities  added  together  over  the  number  of  the 
meeting  must  have  voted  in  favour  of  each  resolution 
This  kind  of  inference  has  by  Sir  W.  Hamilton  been 
said  to  depend  on  ultra-total  distribution  ;  and  the  name 
of  Plurative  Propositions  has  been  proposed  for  all  those 
irhich  give  a  distinct  idea  of  the  fraction  or  number  of  the 
subject  involved  in  the  assertion. 

T.  Spencer  Baynes,  Essay  on  the  new  Analytic  oj 

Logical  Forms;  Edinburgh,  1850. 
Prof.  Bowen's  Treatise  on  Logic  or  the  Laws  of  Pure 

Thought,   Cambridge,   U.   S.    1866   (Triibner   and 

Co.)  gives  a  full  and  excellent  account  of  Hamilton's 

Logic. 


LESSON  XXIII. 
BOOLE'S  SYSTEM  OF  LOGIC. 

IT  would  not  in  the  least  be  possible  to  give  in  an  ele- 
mentary work  a  notion  of  the  system  of  indirect  inference 
first  discovered  by  the  late  Dr  Boole,  the  Professor  of 
Mathematics  at  the  Queen's  College,  Cork.  This  system 
was  founded  as  mentioned  in  the  last  lesson  upon  the 
Quantification  of  the  Predicate,  but  Dr  Boole  regarded 
Logic  as  a  branch  of  Mathematics,  and  believed  that  he 
could  arrive  at  every  possible  inference  by  the  principles 
of  algebra.  The  process  as  actually  employed  by  him 
is  very  obscure  and  difficult ;  and  hardly  any  attempt  to 
introduce  it  into  elementary  text-books  of  Logic  has  yet 
been  made. 

I  have  been  able  to  arrive  at  exactly  the  same  results 


192          BOOLE'S  SYSTEM   OF  LOGIC.        [LESS. 

AS  Dr  Boole  without  the  use  of  any  mathematics;  arui 
though  the  very  simple  process  which  I  am  going  to 
describe  can  hardly  be  said  to  be  strictly  Dr  Boole's 
logic,  it  is  yet  very  similar  to  it  and  can  prove  everything 
that  Dr  Boole  proved.  This  Method  of  Indirect  Inference 
is  founded  upon  the  three  primary  Laws  of  Though! 
stated  in  Lesson  xiv.,  and  the  reader  who  may  have 
thought  them  mere  useless  truisms  will  perhaps  be  sui- 
prised  to  find  how  extensive  and  elegant  a  system  of 
deduction  may  be  derived  from  them. 

The  law  of  excluded  middle  enables  us  to  assert  that 
anything  must  either  have  a  given  quality  or  must  have  it 
not  Thus  if  iron  be  the  thing,  and  combustibility  the 
quality,  anyone  must  see  that 

"Iron  is  either  combustible  or  incombustible." 
This  division  of  alternatives  may  be  repeated  as  often 
as  we  like.  Thus  let  Book  be  the  class  of  things  to  be  di- 
vided, and  English  and  Scientific  two  qualities.  Then  any 
book  must  be  either  English  or  not  English;  again  an 
English  book  must  be  either  Scientific  or  not  Scientific, 
and  the  same  may  be  said  of  books  which  are  not  English 
Thus  we  can  at  once  divide  books  into  four  classes — 

Books,  English  and  Scientific. 

Books,  English  and  not-Scientific. 

Books,  not-English  and  Scientific. 

Books,  not-English  and  not- Scientific. 
This  is  what  we  may  call  an  exhaustive  division  of  the 
class  Books;  for  there  is  no  possible  book  which  does 
not  fall  into  one  division  or  other  of  these  four,  on 
account  of  the  simple  reason,  that  if  it  does  not  fall  into 
ainy  of  the  three  first  it  must  fall  into  the  last.  The  pro- 
cess can  be  repeated  without  end,  as  long  as  any  new 
circumstance  can  be  suggested  as  the  ground  of  division. 
Thus  we  might  divide  each  class  again  according  -as  the 


AXIII.]       BOOLE'S  SYSTEM  OF  LOGIC.         193 

books  are  octavo  or  not  octavo,  bound  or  unbound,  pub- 
lished in  London  or  elsewhere,  and  so  on.  We  shall  call 
Ihis  process  of  twofold  division,  which  is  really  the  pro- 
;ess  of  Dichotomy  mentioned  in  p.  107,  the  development 
tf  a  term,  because  it  enables  us  always  to  develope  the 
itxnost  number  of  alternatives  which  need  be  considered. 
As  a  general  rule  it  is  not  likely  that  all  the  alterna- 
tives thus  unfolded  or  developed  can  exist,  and  the  nexf 
point  is  to  ascertain  how  many  do  or  may  exist  The  Lavi 
of  Contradiction  asserts  that  nothing  can  combine  con- 
tradictory attributes  or  qualities,  and  if  we  meet  with  any 
term  which  is  thus  self-contradictory  we  are  authorized  at 
once  to  strike  it  out  of  the  list  Now  consider  our  old 
example  of  a  syllogism  : 

Iron  is  a  metal ; 
All  metals  are  elements ; 
Therefore  iron  is  an  element 

We  can  readily  prove  this  conclusion  by  the  indirect 
method.     For  if  we  develope  the  term  iron,  we  have  foui 
alternatives;  thus—- 
Iron, metal,  element 
Iron,  metal,  not-element 
Iron,  not- metal,  element 
Iron,  not-metal,  not-element 

But  if  we  compare  each  of  these  alternatives  with  the 
premises  of  the  syllogism,  it  will  be  apparent  that  several 
of  them  are  incapable  of  existing.  Iron,  we  are  informed, 
is  a  metal  Hence  no  class  of  things  "iron,  not-metal" 
can  exist  Thus  we  are  enabled  by  the  first  premise  to 
strike  out  both  of  the  last  two  alternatives  which  combine 
iron  and  not-metal.  The  second  alternative,  again,  com- 
bines metal  and  not-element ;  but  as  the  second  premise 
informs  us  that  "all  metals  are  elements,"  it  must  b« 
struck  out  There  remains,  then,  only  one  alternative 


194  BOOLE'S  SYSTEM  OF  LOGIC.       [LESS 

which  is  capable  of  existing  if  the  premises  be  true,  and  a  j 
there  cannot  conceivably  be  more  alternatives  than  those 
considered,  it  follows  demonstratively  that  iron  occurs 
only  in  combination  with  the  qualities  of  metal  and  ele- 
ment, or,  in  brief,  that  it  is  an  element 

We  can,  however,  prove  not  only  the  ordinary  syllo- 
gistic conclusion,  but  any  other  conclusion  which  can  b< 
drawn  from  the  same  premises ;  the  syllogistic  conclusion 
is  in  fact  only  one  out  of  many  which  can  usually  be  ob- 
tained from  given  premises.     Suppose,  for  instance,  that 
we  wish  to  know  what  is  the  nature  of  the  term  or  class 
not-element,  so  far  as  we  can  learn  it  from  the  premises 
just  considered.     We  can  develope  the  alternatives  of  this 
term,  just  as  we  did  those  of  iron,  and  get  the  following— 
Not-element,  iron,  metal. 
Not-element,  iron,  not-metaL 
Not-element,  not-iron,  metal. 
Not-clement,  not-iron,  not-metal 

Compare  these  combinations  as  before  with  the  premises. 
The  first  it  is  easily  seen  cannot  exist,  because  all  metals 
are  elements ;  for  the  same  reason  the  third  cannot  exist ; 
the  second  is  likewise  excluded,  because  iron  is  a  metal 
and  cannot  exist  in  combination  with  the  qualities  of  not- 
metaL  Hence  there  remains  only  one  combination  to 
represent  the  class  desired — namely, 

Not-element,  not-iron,  not-metaL 
Thus  we  learn  from  the  premises  that  every  not-ele 
eaent  is  not  a  metal  and  is  not  iron. 

As  another  example  of  this  kind  of  deductive  procesi 
I  will  take  a  case  of  the  Disjunctive  Syllogism,  in  the  ne 
gatire  mood,  as  follows : — 

A  fungus  is  either  plant  or  animal , 
A  fungus  is  not  an  animal ; 
Therefore  it  is  a  plant 


ttlil.]      BOOL&S  SYSTEM  OF  LOGIC.  ifc 

Now  if  we  develope  all  the  possible  ways  in  which 
<ungus,  plant  and  animal  can  be  combined  together,  we 
obtain  for  the  term  fungus — 

(1)  Fungus,  plant,  animal 

(2)  Fungus,  plant,  not-animal 

(3)  Fungus,  not-plant,  animal 

(4)  Fungus,  not-plant,  not-animal 

Of  these  however  the  4th  cannot  exist  because  by 
the  premise  a  fungus  must  be  a  plant,  or  if  not  a  plant  an 
animal  The  ist  and  3rd  again  cannot  exist  because  tht 
minor  premise  informs  us  that  a  fungus  is  not  an  animal 
There  remains  then  only  the  second  combination, 

Fungus,  plant,  not-animal, 

from    which   we    learn  the    syllogistic  conclusion   that 
"a  fungus  is  a  plant" 

The  chief  excellence  of  this  mode  of  deduction  consists 
in  the  fact  that  it  is  not  restricted  to  any  definite  series 
of  forms  like  the  syllogism,  but  is  applicable,  without  any 
additional  rules,  to  all  kinds  of  propositions  or  problems 
which  can  be  conceived  and  stated.  There  may  be  any 
number  of  premises,  and  they  may  contain  any  number  of 
terms ;  all  we  have  to  do  to  obtain  any  possible  inference 
is  to  develope  the  term  required  into  all  its  alternatives 
and  then  to  examine  how  many  of  these  agree  with  the  pre- 
mises. What  remain  after  this  examination  necessarily 
form  the  description  of  the  term.  The  only  inconvenience 
of  the  method  is  that,  as  the  number  of  terms  increases, 
the  number  of  alternatives  to  be  examined  increases  very 
rapidly,  and  it  soon  becomes  tedious  to  write  them  all  out 
This  work  may  be  abbreviated  if  we  substitute  single 
letters  to  stand  for  the  terms,  somewhat  as  in  algebra; 
thus  we  may  take  A,B,  C,  D,  &c.,  to  stand  for  the  affirm 
ative  terms,  and  a,  £,  <r,  d,  &<x,  for  the  corresponding  nega 
live  ones.  Let  us  take  as  a  first  example  the  premises— 

13-2 


196  BOOLE'S  SYST&M   OF  LOGIC.       [LES1 

Organic  substance  is  either  vegetable  or  animal 
Vegetable  substance  consists  mainly  of  carbon,  hydrogeL 

and  nitrogen. 
Animal  substance  consists  mainly  of  carbon,  hydrogen, 

and  nitrogen. 

It  would  take  a  long  time  to  write  out  all  the  combi- 
nations of  the  four  terms  occurring  in  the  above ;  but  tf 
ire  substitute  letters  as  follows — 

A—  organic  substance, 

B= vegetable  substance, 

C=  animal  substance, 

D= consisting  mainly  of  carbon,  hydrogen,  and 

nitrogen, 

we  can  readily  represent  all  the  combinations  which  can 
belong  to  the  term  A. 

(1)  ABCD  AbCD  (5) 

(2)  ABCd  AbCd  (6) 

(3)  ABcD  AbcD  (7) 

(4)  ABcd  Abed  (8) 

Now  the   premises  amount  to  the  statements,  that 
A  must  be  either  B  or  Ct 
B  must  be  Dt 
C  must  be  D. 

The  combinations  (7)  and  (8)  are  inconsistent  with  .the 
first  premise ;  the  combinations  (2)  and  (4)  with  the  second 
premise;  and  (6)  is  inconsistent  with  rhe  third  premise, 
There  remain  only, 

ABCD 
ABfD 
AbCD. 

Whence  we  learn  at  once  that  "organic  substance  (A% 
always  consists  mainly  of  carbon,  hydrogen  and  nitrogen,* 


xxill. J      BOOLE'S  SYSTEM  OF  LOGIC.  197 

because  it  always  occurs  in  connexion  with  D.  The  readef 
may  perhaps  notice  that  the  term  A  BCD  implies  that  or- 
ganic substance  may  be  both  vegetable  (ff)  and  animal  (C\ 
If  the  first  premise  be  interpreted  as  meaning  that  this  is 
not  possible,  of  course  this  combination  should  also  be 
struck  out.  It  is  an  unsettled  point  whether  the  alter- 
natives of  a  disjunctive  proposition  can  coexist  or  not 
(see  p.  1 66),  but  I  much  prefer  the  opinion  that  they 
can;  and  as  a  matter  of  fact  it  is  quite  likely  that  there 
exist  very  simple  kinds  of  living  beings,  which  cannot  be 
distinctly  asserted  to  be  vegetable  only  or  animal  only, 
but  partake  of  the  nature  of  each. 

As  a  more  complicated  problem  to  shew  the  powers  oi 
this  system,  let  us  consider  the  premises  which  were 
treated  by  Dr  Boole  in  his  Laws  of  Thought,  p.  125,  as 
follows : 

"  Similar  figures  consist  of  all  whose  corresponding 
angles  are  equal,  and  whose  corresponding  sides  are 
proportional 

Triangles  whose  corresponding  angles  are  equal  have 
their  corresponding  sides  proportional ;  and  vice  versa. 

Triangles  whose  corresponding  sides  are  proportional 
have  their  corresponding  angles  equal." 

Now  if  we  take  our  symbol  letters  as  follows : 

A  =  similar  figure, 
B— triangle, 

C=  having  corresponding  angles  equal, 
D= having  corresponding  sides  proportional, 
the  premises  will  be  seen  to  amount  to  the  statements  j&at 

A  is  identical  with  CD, 
and  that 

BC  is  identical  with  BD; 
in  other  words,  all  A's  ought  to  be  CD's,  CD's  ought  U 


198  &OOL&S  SYSTEM  OF  LOGIC.        [LESS 

be  A's,  all  BCs  ought  to  be  B&s  and  all  8Z?s  ought  to 
be.ffC's. 

The  possible  combinations  in  which  the  letters  may  1x 
united  are  16  in  number  and  are  shewn  in  the  following 
'able: 

ABCD  aBCD 

ABCd  aBCd 

ABcD  aBcD 

ABcd  aBcd 

AbCD  abCD 

AbCd  abCd 

AbcD  abcD 

Abed  abed 

Comparing  each  of  these  combinations  with  the  premise) 
we  see  that  ABCd,  ABcD,  ABcd,  and  others,  are  to  U 
struck  out  because  every  A  is  also  to  be  CD.  The  com- 
binations aBCD  and  abCD  are  struck  out  because  ever) 
CD  should  also  be  A.  Again,  aBCd  is  inconsistent  with 
the  condition  that  every  BC  is  also  to  be  BD\  and  ii 
the  reader  carefully  follows  out  the  same  process  of  ex- 
amination, there  will  remain  only  six  combinations,  which 
agree  with  all  the  premises,  thus — 

ABCD  aBcd 

AbCD  abCd 

abcD 
abed 

From  these  combinations  we  can  draw  any  description 
ire  like  of  the  classes  of  things  agreeing  with  the  premises, 
The  class  A  or  similar  figures  is  represented  by  only  two 
combinations  or  alternatives ;  the  negative  class  a  01 
dissimilar  figures,  by  four  combinations,  whence  wr  may 
Jraw  the  following  conclusion:  "Dissimilar  figure*  con 
•1st  of  all  triangles  which  have  not  their  corresponding 
angles  equal,  and  sides  proportional  (aBcd],  and  of  aO 


XXIIL]      3OOL&S  SYSTEM  OF  LOGIC  19? 

figures,  not  being  triangles,  which  have  either  their  angles 
equal  and  sides  not  proportional  (abCtT),  or  their  coi> 
responding  sides  proportional  and  angles  not  equal 
(abcD\  or  neither  their  corresponding  angles  equal  noi 
corresponding  sides  proportional  (abed)" 

In  performing  this  method  of  inference  it  is  soon  seeu 
to  proceed  in  a  very  simple  mechanical  manner,  and  th< 
only  inconvenience  is  the  large  number  of  alternatives  01 
combinations  to  be  examined.  I  have,  therefore,  devised 
several  modes  by  which  the  labour  can  be  decreased; 
the  simplest  of  these  consists  in  engraving  the  series 
of  1 6  combinations  on  the  opposite  page,  which  occur 
over  and  over  again  in  problems,  with  larger  and  smaller 
sets,  upon  a  common  writing  slate,  so  that  the  excluded 
ones  may  be  readily  struck  out  with  a  common  slate 
pencil,  and  yet  the  series  may  be  employed  again  for  any 
future  logical  question.  A  second  device,  which  I  have 
called  the  "Logical  abacus,"  is  constructed  by  printing  the 
letters  upon  slips  of  wood  furnished  with  pins,  contrived 
so  that  any  part  or  class  of  the  combinations  can  be 
picked  out  mechanically  with  very  little  trouble ;  and  a 
logical  problem  is  thus  solved  by  the  hand,  rather  than 
by  the  head  More  recently  however  I  have  reduced  the 
system  to  a  completely  mechanical  form,  and  have  thus 
embodied  the  whole  of  the  indirect  process  of  inference 
in  what  may  be  called  a  Logical  Machine.  In  the  front 
of  the  machine  are  seen  certain  moveable  wooden  rods 
carrying  the  set  of  16  combinations  of  letters  which  are 
seen  on  the  preceding  page.  At  the  foot  are  21  keys  like 
those  of  a  piano;  eight  keys  towards  the  left  hand  are 
marked  with  the  letters  A,  a,  By  b,  C,  ft  D,  d,  and  are 
intended  to  represent  these  terms  when  occurring  in  the 
subject  of  a  proposition.  Eight  other  keys  towards  the 
right  hand  represent  the  same  letters  or  terms  when  oc- 
curring in  the  predicate.  The  copula  of  a  proposition  if 


200  BOOLES  SYSTEM  OF  LOGIC.       [LI* 

represented  by  a  key  in  the  middle  of  the  series »  the  ful 
stop  by  one  to  the  extreme  right,  while  there  are  two  othei 
keys  which  serve  for  the  disjunctive  conjunction  ort  ac« 
cording  as  it  occurs  in  subject  or  predicate.  Now  if  the 
letters  be  taken  to  stand  for  the  terms  of  a  syllogism  or 
any  other  logical  argument,  and  the  keys  of  the  instru- 
ment be  pressed  exactly  in  the  order  corresponding  to  the 
words  of  the  premises,  the  16  combinations  will  be  so 
selected  and  arranged  thereby  that  at  the  end  only  the 
possible  combinations  will  remain  in  view.  Any  question 
can  then  be  asked  of  the  machine,  and  an  infallible  answei 
will  be  obtained  from  the  combinations  remaining.  The 
internal  construction  of  the  machine  is  such,  therefore,  as 
actually  to  perform  the  work  of  inference  which,  in  Dr 
Boole's  system,  was  performed  by  a  very  complicated 
mathematical  calculation.  It  should  be  added,  that  there 
is  one  remaining  key  to  the  extreme  left  which  has  the 
effect  of  obliterating  all  previous  operations  and  restoring 
all  the  combinations  to  their  original  place,  so  that  the 
machine  is  then  ready  for  the  performance  of  any  new 
problem. 

An  account  of  this  logical  machine  may  be  found  in 
the  Proceedings  of  the  Royal  Society  for  Jan.  2oth,  1870, 
the  machine  having  on  that  day  been  exhibited  in  action  to 
the  Fellows  of  the  Society.  The  principles  of  the  method 
}f  inference  here  described  are  more  completely  stated  in 
The  Substitution  of  Similar s*,  and  the  Pure  Logic\,  which 
[  published  in  the  years  1869  and  1864.  I  may  add,  that 
:hr  first-named  of  these  works  contains  certain  views  as 
>o  the  real  nature  of  the  process  of  inference  which  I  do 

'  Ttu  Substitution  of  Similars,  the  true  Principle  of  Reason- 
nf,  derrved  from  a  modification  of  Aristotle's  Dictum.  Mac- 
aulLui  and  Co.  1869. 

t  Purt  Lofic,  or  the  Logic  of  Quality  apart  from  Quantity  >&* 
Reward  Stanford,  Charing  Cross. 


XXIIL]      BOOLE^S  SYSTEM  OF  LOGIC.  aoi 

not  think  it  desirable  to  introduce  into  an  elementary  work 
like  the  present,  on  account  of  their  speculative  character. 
The  process  of  inference,  on  the  other  hand,  which  I  ha/c 
derived  from  Boole's  system  is  of  so  self-evident  a  charac- 
ter, and  is  so  clearly  proved  to  be  true  by  its  reduction  to 
a  mechanical  form,  that  I  do  not  hesitate  to  bring  it  to  the 
reader's  notice. 

George  Boole,  Mathematical  Analysis  of  Logic,  1847 
An  Investigation  of  the  Laws  of  Thought.     Londor 
Walton  and  Maberly,  1854. 


LESSON   XXIV. 
ON   METHOD,  ANALYSIS  AND  SYNTHESIS. 

IT  has  been  held  by  many  writers  on  Logic  that,  in  addi- 
tion to  the  three  parts  of  logical  doctrine  which  treat 
successively  of  Terms,  Propositions  and  Syllogisms,  there 
was  a  fourth  part,  which  treats  of  method.  Just  as  the 
doctrine  of  Judgment  considers  the  arranging  of  terms 
and  their  combination  into  Propositions,  and  the  doc- 
trine of  Syllogism  considers  the  arranging  of  propositions 
that  they  may  form  arguments,  so  there  should  in  like 
manner  be  a  fourth  part,  called  Method,  which  should 
govern  the  arrangement  of  syllogisms  and  their  combina- 
tion into  a  complete  discourse.  Method  is  accordingly 
defined  as  consisting  in  such  a  disposition  oj  the  parts  o) 
m  discourse  that  the  whole  may  be  most  easily  intelligible. 
The  celebrated  Peter  Ramus,  who  perished  in  the 
massacre  of  St  Bartholomew,  first  proposed  to  make 
method  in  this  manner  a  part  of  the  science  of  Logic ;  but 


2t*  ON  METHOD,  ANALYSIS          [LESS 

it  may  well  be  doubted  whether  any  definite  set  of  rulej 
or  principles  can  be  given  to  guide  us  in  the  arrangement 
of  "arguments.  Every  different  discourse  must  consist  oi 
arguments  arranged  in  accordance  wilh  the  peculiar  nature 
af  the  subject ;  and  no  general  rules  can  be  given  for  treat- 
ing things  which  are  infinitely  various  in  the  mode  of  treat- 
ment required.  Accordingly  the  supposed  general  rules 
of  method  are  no  better  than  truisms,  that  is,  they  tell  us 
nothing  more  than  we  must  be  supposed  to  know  before- 
hand Thus,  we  are  instructed  in  composing  any  dis- 
course to  be  careful  that — 

1.  Nothing  should  be  wanting  or  redundant. 

2.  The  separate  parts  should  agree  with  each  other. 

3.  Nothing  should  be  treated  unless  it  is  suitable  to 
the  subject  or  purpose. 

4.  The  separate  parts  should  be  connected  by  suit- 
able transitions. 

But  it  is  evident  that  the  whole  difficulty  consists  in 
deciding  what  is  wanting  or  redundant,  suitable  or  con- 
sistent. Rules  of  this  kind  simply  tell  us  to  do  what  we 
ought  to  do,  without  defining  what  that  is. 

There  exist  nevertheless  certain  general  modes  of 
treating  any  subject  which  can  be  clearly  distinguished, 
and  should  be  well  understood  by  the  logical  student. 
Logic  cannot  teach  him  exactly  how  and  when  to  use 
each  kind  of  method,  but  it  can  teach  him  the  natures 
and  powers  of  the  methods,  so  that  he  will  be  more  Ukeiy 
to  use  them  rightly.  We  must  distinguish, 

1.  The  method  of  discovery, 

2.  The  method  of  instruction. 

The  method  of  discovery  is  employed  in  the  acquisi- 
tion of  knowledge,  and  really  consists  in  those  processes 
af  inference  and  induction,  by  which  general  truths  ara 
ascertained  from  the  collection  and  examination  of  par- 


AND  SYNTHESIS.  205 

ticular  facts.  This  method  will  be  the  subject  of  most  ol 
our  remaining  Lessons.  The  second  method  only  applies 
when  knowledge  has  already  been  acquired  and  express- 
ed in  the  form  of  general  laws,  rules,  principles  or  truths 
jo  that  we  have  only  to  make  ourselves  acquainted  will 
hese  and  observe  the  due  mode  of  applying  them  tt 
particular  cases,  in  order  to  possess  a  complete  acquaint 
ance  with  the  subject 

A  student,  for  example,  in  learning  Latin,  Greek, 
French,  German,  or  any  well-known  language,  receives  a 
complete  Grammar  and  Syntax  setting  forth  *he  whole  of 
the  principles,  rules  and  nature  of  the  language.  He 
receives  these  instructions,  and  takes  them  to  be  true  on 
the  authority  of  the  teacher,  or  the  writer  of  the  book; 
and  after  rendering  them  familiar  to  his  mind  he  has 
nothing  to  do  but  to  combine  and  apply  the  rules  in  read- 
ing or  composing  the  language.  He  follows,  in  short, 
the  method  of  Instruction.  But  this  is  an  entirely  differ- 
ent and  opposite  process  to  that  which  the  scholar  must 
pursue  who  has  received  some  writings  in  an  unknown 
language,  and  is  endeavouring  to  make  out  the  alpha- 
bet, words,  grammar,  and  syntax  of  the  language.  He 
possesses  not  the  laws  of  grammar,  but  words  and  sen- 
tences obeying  those  laws,  and  he  has  to  detect  the 
laws  if  possible  by  observing  their  effects  on  the  written 
language.  He  pursues,  in  short,  the  method  of  discovery 
consisting  in  a  tedious  comparison  of  letters,  words,  and 
phrases,  such  as  shall  disclose  the  more  frequent  combi- 
nations and  forms  in  which  they  occur.  The  process 
would  be  a  strictly  inductive  one,  such  as  I  shall  partially 
exemplify  in  the  Lessons  on  Induction ;  but  it  is  far  more 
difficult  than  the  method  of  Instruction,  and  depends  to  a 
great  extent  on  the  happy  use  of  conjecture  and  hypothesis 
which  demands  a  certain  skill  and  inventive  ability. 

Exactly  the  same  may  be  said  of  the  investigation  o( 


so4  ON  METHOD,  ANALYSIS  [LESi 

natural  things  and  events.  The  principles  of  mechanic* 
ol  the  lever,  inclined  plane,  and  other  Mechanical  Powers 
or  the  Laws  of  Motion,  seem  comparatively  simple  and 
obvious  as  explained  to  us  in  books  of  instruction.  But 
the  early  philosophers  did  not  possess  such  books ;  they 
had  only  the  Book  of  Nature,  in  which  is  set  forth  not 
the  laws  but  the  results  of  the  laws,  and  it  was  only 
after  the  most  patient  and  skilful  investigation,  and  after 
hundreds  of  mistakes,  that  those  laws  were .  ascertained 
It  is  very  easy  now  to  understand  the  Copernican  system 
of  Astronomy,  which  represents  the  planets  as  revolving 
round  the  sun  in  orbits  of  various  magnitude.  Once  know- 
ing the  theory  we  can  readily  see  why  the  planets  have 
such  various  movements  and  positions,  and  why  they 
sometimes  stand  still ;  it  is  easy  to  see,  too,  why  in  ad- 
dition to  their  own  proper  motions  they  all  go  round  the 
earth  apparently  every  day  in  consequence  of  the  earth's 
diurnal  rotation.  But  all  these  changes  were  exceedingly 
puzzling  to  the  ancients,  who  regarded  the  earth  as  stand- 
ing still. 

The  method  of  discovery  thus  begins  with  facts  ap- 
parent to  the  senses,  and  has  the  difficult  task  of  detecting 
those  universal  laws  or  general  principles  which  can  only 
be  comprehended  by  intellect.  It  has  been  aptly  said 
that  the  method  of  discovery  thus  proceeds  front  thing* 
better  known  to  us,  or  our  senses  (nobis  notiord),  to  those 
which  are  more  simple  or  better  known  in  nature  (notiora 
nature).  The  method  of  Instruction  proceeds  in  the 
opposite  direction,  beginning  with  the  things  notiora 
nature,  and  proceeding  to  show  or  explain  the  things 
nobis  notiora.  The  difference  is  almost  like  that  between 
hiding  and  seeking.  He  who  has  hidden  a  thing  knows 
where  to  find  it;  but  this  is  not  the  position  of  a  discoverer, 
who  has  no  clue  except  such  as  he  may  meet  in  his  own 
diligent  and  sagacious  search. 


AND  SYNTHESIS.  903 

Closely  corresponding  to  the  distinction  between  the 
methods  of  Discovery  and  Instruction  is  that  between 
the  methods  of  Analysis  and  Synthesis.  It  is  very  im- 
portant indeed  that  the  reader  should  clearly  apprehend 
the  meanings  of  these  terms  in  their  several  applications. 
Analysis  is  the  process  of  separating  a  whole  into  its 
parts,  and  synthesis  the  combination  ot  parts  into  a 
whole.  The  analytical  chemist,  who  receives  a  piece  ol 
mineral  for  examination,  may  be  able  to  separate  com- 
pletely the  several  chemical  elements  of  which  it  is 
composed  and  ascertain  their  nature  and  comparative 
quantities ;  this  is  chemical  analysis.  In  other  cases  the 
chemist  mixes  together  carefully  weighed  quantities  of 
certain  simple  substances  and  combines  them  into  a  new 
compound  substance ;  this  is  chemical  synthesis.  Logical 
analysis  and  synthesis  must  not  be  confused  with  the 
physical  actions,  but  they  are  nevertheless  actions  ol 
mind  of  an  analogous  character. 

In  logical  synthesis  we  begin  with  the  simplest  possible 
notions  or  ideas,  and  combine  them  together.  We  have 
the  best  possible  example  in  the  elements  of  Geometry 
In  Euclid  we  begin  with  certain  simple  notions  of  points, 
straight  lines,  angles,  right  angles,  circles,  &c.  Putting 
together  three  straight  lines  we  make  a  triangle ;  joining 
to  this  the  notion  of  a  right-angle,  we  form  the  notion  of 
a  right-angled  triangle.  Joining  four  other  equal  lines  at 
right  angles  to  each  other  we  gain  the  idea  of  a  square, 
and  if  we  then  conceive  such  a  square  to  be  formed  upon 
each  of  the  sides  of  a  right-angled  triangle,  and  reason 
from  the  necessary  qualities  of  these  figures,  we  discover 
that  the  two  squares  upon  the  sides  containing  the  right 
angle  must  together  be  exactly  equal  to  the  square  upon 
the  third  side,  as  shewn  in  the  47th  Proposition  ol 
Euclid's  first  book.  This  is  a  perfect  instance  ol  com* 
oining  simple  ideas  into  more  complex  ones. 


•06  ON  METHOD,  ANALYSIS          [LESS 

We  have  often,  however,  in  Geometry  to  pursue  the 
opposite  course  of  Analysis.  A  complicated  geometrical 
figure  may  be  given  to  us,  and  we  may  have,  in  order  to 
prove  the  properties  which  it  possesses,  to  resolve  it  inte 
its  separate  parts,  and  to  consider  the  properties  of  thost 
parts  each  distinct  from  the  others. 

A  similar  distinction  between  the  analytical  and  syn 
thetic  methods  can  be  traced  throughout  the  natura 
sciences.  By  keeping  exact  registers  of  the  appearance 
and  changes  of  the  weather  we  may  readily  acquire  at 
immense  collection  of  facts,  each  such  recorded  fact 
implying  a  multitude  of  different  circumstances  occurring 
together.  Thus  in  any  storm  or  shower  of  rain  we  have 
to  consider  the  direction  and  force  of  the  wind ;  the  tem- 
perature and  moistness  of  the  air ;  the  height  and  forms  ol 
the  clouds;  the  quantity  of  rain  which  falls,  or  the  light- 
ning and  thunder  which  occur  with  it.  If  we  proceed  by 
analysis  only  to  explain  the  changes  of  the  weather  we 
should  have  to  try  resolving  each  storm  or  change  of 
weather  into  its  separate  circumstances,  and  comparing 
each  with  every  other  to  discover  what  circumstances 
usually  go  together.  We  might  thus  ascertain  no  doubt 
with  considerable  certainty  what  kinds  of  clouds,  and 
what  changes  of  the  wind,  temperature,  moisture,  &c^ 
usually  precede  any  kind  of  storm,  and  we  might  even  in 
time  give  some  imperfect  explanation  of  what  takes  place 
in  the  atmosphere. 

But  we  might  also  apply  with  advantage  the  syn- 
thetical method.  By  previous  chemical  investigations  we 
know  that  the  atmosphere  consists  mainly  of  the  two 
fixed  gases,  oxygen  and  nitrogen,  with  the  vapour  of 
irater,  the  latter  being  very  variable  in  quantity.  We 
can  try  experimentally  what  takes  place  when  portions 
of  such  air  of  various  degrees  of  moistness  are  com- 
pressed or  allowed  to  expand,  or  are  mixed  togethei,  at 


XXIV.]  AND  SYNTHESIS.  so? 

often  happens  in  the  atmosphere.  It  is  thus  discovered 
that  whenever  moist  air  is  allowed  to  expand  cloud 
is  produced,  and  it  may  be  drops  of  rain.  Dr  Hut- 
ton,  too,  found  that  whenever  cold  moist  air  is  mixed 
with  warm  moist  air  cloud  is  again  produced.  We  can 
safely  argue  from  such  small  experiments  to  what  takei 
place  in  the  atmosphere.  Putting  together  synthetically, 
from  the  sciences  of  chemistry,  mechanics,  and  electricity,, 
all  that  we  know  of  air,  wind,  cloud  and  lightning,  we  are 
able  to  explain  what  takes  place  in  a  thunder-storm  far 
more  completely  than  we  could  do  by  merely  observing 
directly  what  happens  in  the  storm.  We  are  here  how- 
ever anticipating  the  methods  of  inductive  investigation, 
which  we  must  consider  in  the  following  lessons.  It  will 
appear  that  Induction  is  equivalent  to  analysis,  and  that 
the  deductive  kinds  of  reasoning  which  we  have  treated 
in  prior  lessons  are  of  a  synthetic  character. 

It  has  been  said  that  the  synthetic  method  usually 
corresponds  to  the  method  of  instruction  and  the  analytic 
method  to  that  of  discovery.  But  it  may  be  possible  to 
discover  new  truths  by  synthesis  and  to  teach  old  ones 
by  analysis.  Sir  John  Herschel  in  his  well-known  Out- 
lines of  Astronomy  partially  adopts  the  analytic  method; 
he  supposes  a  spectator  in  the  first  place  to  survey  the 
appearances  of  the  heavenly  bodies  and  the  surface  of 
the  earth,  and  to  seek  an  explanation;  he  then  leads 
him  through  a  course  of  arguments  to  show  ;hat  these 
appearances  really  indicate  the  rotundity  of  the  earth,  its 
revolution  about  its  own  axis  and  round  the  sun,  and  its 
subordinate  position  as  one  of  the  smaller  planets  of  the 
solar  system.  Mr  Norman  Lockyer's  Elementary  Lessons 
in  Astronomy  is  a  clear  example  of  the  synthetic  method 
of  instruction  ;  for  he  commences  by  describing  the  sun, 
the  centre  of  the  system,  and  successively  adds  the  planet! 
and  other  members  of  the  system,  until  at  last  we  havf 


208  ON  METHOD,  ANALYSIS  [LESi 

the  complete  picture ;  and  the  reader  who  has  temporarily 
received  everything  on  the  writer's  authority,  sees  that 
the  description  corresponds  with  the  truth.  Each  method, 
it  must  be  allowed,  has  its  own  advantages. 

It  must  be  carefully  observed  that  the  meaning  oi 
Analysis,  and  therefore  that  of  synthesis,  varies  according 
as  we  look  to  the  intension  or  extension  of  terms.  To 
divide  or  analyse  a  class  of  things  in  extension  I  must  add 
a  quality  or  difference.  Thus  I  divide  the  class  organism 
when  I  add  the  quality  vegetable p,  and  separate  vegetable 
organism  from  what  is  not  vegetable.  Analysis  in  exten- 
sion is  therefore  the  same  process  as  synthesis  in  inten^ 
•Ion ;  and  vice  versd,  whenever  I  separate  or  analyse  a 
group  of  qualities  each  pan  belongs  to  a  larger  class  oi 
things  in  extension.  When  I  analyse  the  notion  vegetable 
organism,  and  regard  the  notion  organism  apart  from 
vegetable,  it  is  apparent  that  I  really  add  the  whole  class 
of  animal  organisms  to  the  class  I  am  considering — so 
that  analysis  in  intension  is  synthesis  in  extension.  The 
reader  who  has  well  considered  the  contents  of  Lessons 
V.  and  XII.  will  probably  see  that  this  connection  of  the 
two  processes  is  only  a  re-statement  of  the  law,  (p.  40), 
that  "as  the  intension  of  a  term  is  increased  the  extension 
is  decreased." 

To  express  the  difference  between  knowledge  derived 
deductively  and  that  obtained  inductively  the  Latin 
phrases  a  priori  and  a  posteriori  are  often  used.  By 
A  priori  reasoning  we  mean  argument  based  on  truthi 
previously  known  ;  A  posteriori  reasoning,  on  the  contrary, 
proceeds  to  infer  from  the  consequences  of  a  general 
truth  what  that  general  truth  is.  Many  philosophers  con- 
sider that  the  mind  is  naturally  in  possession  of  certain 
laws  or  truths  which  it  must  recognise  in  every  act  of 
thought ;  all  such,  if  they  exist,  would  be  a  priori  truths. 
It  cannot  be  doubted,  for  instance,  that  we  must  always 


KXIV.]  AND  SYNTHESIS.  209 

recognise  m  thought  the  three  Primary  Laws  of  Thought 
considered  in  Lesson  xiv.  We  have  there  an  a  priori 
knowledge  that  "matter  cannot  both  have  weight  and  be 
without  weight,"  or  that  "every  thing  must  be  either  self- 
hiininous  or  'not  self-lutninous."  But  there  is  no  law  of 
thought  which  can  oblige  us  to  think  that  matter  has 
weight,  and  luminous  ether  has  not  weight ;  that  Jupitei 
and  Venus  are  not  self-luminous,  but  that  comets  are  to 
some  extent  self-luminous.  These  are  facts  which  are  no 
doubt  necessary  consequences  of  the  laws  of  nature  and 
the  general  constitution  of  the  world ;  but  as  we  are  not 
naturally  acquainted  with  all  the  secrets  of  creation,  we 
have  to  learn  them  by  observation,  or  by  the  a  posteriori 
method. 

It  is  not  however  usual  at  the  present  time  to  restrict 
the  name  a  priori  to  truths  obtained  altogether  without 
recourse  to  observation.  Knowledge  may  originally  be 
of  an  a  posteriori  origin,  and  yet  having  been  long 
in  possession,  and  having  acquired  the  greatest  certainty, 
it  may  be  the  ground  of  deductions,  and  may  then  be  said 
to  give  a  priori  knowledge.  Thus  it  is  now  believed  by 
all  scientific  men  that  force  cannot  be  created  or  destroy- 
ed by  any  of  the  processes  of  nature.  If  this  be  true  the 
force  which  disappears  when  a  bullet  strikes  a  target  must 
be  converted  into  something  else,  and  on  a  priori  grounds 
we  may  assert  that  heat  will  be  the  result.  It  is  true  that 
we  might  easily  learn  the  same  truth  a  posteriori,  by 
picking  uv  portions  of  a  bullet  which  has  just  struck  a 
target  ana  observing  that  they  are  warm.  But  there  is  a 
great  advantage  in  a  priori  knowledge ;  we  can  often 
apply  it  in  cases  where  experiment  or  observation  would 
be  difficult.  If  I  lift  a  stone  and  then  drop  it,  the  most 
delicate  instruments  could  hardly  show  that  the  stone 
was  heated  by  striking  the  earth ;  yet  on  a  priori  grounds 
I  know  that  it  must  have  been  so,  and  can  easily  calcu- 

14 


210  PERFECT  INDUCTION  AND        (LESS 

late  the  amount  of  heat  produced.  Similarly  we  know, 
without  the  trouble  of  observation,  that  the  Falls  of  Ni- 
agara and  all  other  waterfalls  produce  heat  This  is 
fairly  an  instance  of  a  priori  knowledge  because  no  one 
that  I  have  heard  of  has  tried  the  fact  or  proved  it  a  pos* 
ieriorij  nevertheless  the  knowledge  is  originally  founded 
on  the  experiments  of  Mr  Joule,  who  observed  in  certain 
well-chosen  cases  how  much  force  is  equivalent  to  a 
certain  amount  of  heat.  The  reader,  however,  should 
take  care  not  to  confuse  the  meaning  of  ct  priori  thus 
explained  with  that  given  to  the  words  by  the  philoso- 
phers who  hold  the  mind  to  be  in  the  possession  of  know- 
ledge independently  of  all  observation. 

It  is  not  difficult  to  see  that  the  a  priori  method  is 
equivalent  to  the  synthetic  method  (see  p.  205)  considered 
in  intension,  the  a  posteriori  method  of  course  being  equi- 
valent to  the  analytic  method.  But  the  same  difference  is 
really  expressed  in  the  words  deductive  and  inductive; 
and  we  shall  frequently  need  to  consider  it  in  the  following 
lessons. 

For  general  remarks  upon  Method  see  the  Port  Roytl 
Logic,  Part  iv. 


LESSON    XXV. 

PERFECT  INDUCTION  AND  THE  INDUCTIVE 
SYLLOGISM. 

Wl  have  in  previous  lessons  considered  deductive  rea- 
soning, which  consists  in  combining  two  or  more  genera] 
propositions  synthetically,  and  thus  arriving  at  a  con- 
clusion which  is  a  proposition  or  truth  of  less  generality 


xxv.]       THE  INDUCTIVE  SYLLOGISM.          211 

than  the  premises,  that  is  to  say,  it  applies  to  fewer  indi- 
vidual instances  than  the  separate  premises  from  which 
it  was  inferred.  When  I  combine  the  general  truth  that 
"  metals  are  good  conductors  of  heat,"  with  the  truth  that 
"aluminium  is  a  metal,"  I  am  enabled  by  a  syllogism  in 
the  mood  Barbara  to  infer  that  "  aluminium  is  a  good  con- 
ductor of  heat."  As  this  is  a  proposition  concerning  one 
metal  only,  it  is  evidently  less  general  than  the  premise, 
which  referred  to  all  metals  whatsoever.  In  induction,  on 
the  contrary,  we  proceed  from  less  general,  or  even  from 
individual  facts,  to  more  general  propositions,  truths,  or, 
as  we  shall  often  call  them,  Laws  of  Nature.  When  it  is 
known  that  Mercury  moves  in  an  elliptic  orbit  round  the 
Sun,  as  also  Venus,  the  Earth,  Mars,  Jupiter,  &c.,  we  are 
able  to  arrive  at  the  simple  and  general  truth  that  "  all  the 
planets  move  in  elliptic  orbits  round  the  sun."  This  is 
an  example  of  an  inductive  process  of  reasoning. 

It  is  true  that  we  may  reason  without  rendering  our 
conclusion  either  more  or  less  general  than  the  premises, 
as  in  the  following  : — 

Snowdon  is  the  highest  mountain  in  England  or  Wales. 

Snowdon  is  not  so  high  as  Ben  Nevis. 

Therefore  the  highest  mountain  in  England  or  Wales  is 

not  so  high  as  Ben  Nevis. 
Again : 

Lithium  is  the  lightest  metal  known. 
Lithium  is  the  metal  indicated  by  one  bright  red  line  in 

the  spectrum*. 
Therefore  the  lightest  metal  known  is  the  metal  indicated 

by  a  spectrum  of  one  bright  red  line. 

In  these  examples  all  the  propositions  are  singular 
propositions,  and  merely  assert  the  identity  of  singular 

*  Roscoe's  Lessons  in  Elementary  Chemistry,  p.  199. 

14—2 


fli  PERFECT  INDUCTION  AND 

terms,  so  that  there  is  no  alteration  of  generality.  Each 
conclusion  applies  to  just  such  an  object  as  each  of  the 
premises  applies  to.  To  this  kind  of  reasoning  the  apt 
name  of  Traduction  has  been  given. 

Induction  is  a  much  more  difficult  and  more  important 
rind  of  reasoning  process  than  Traduction  or  even  Deduc- 
tion ;  for  it  is  engaged  in  detecting  the  general  laws  or 
uniformities,  the  relations  of  cause  and  effect,  or  hi  short 
ail  the  general  truths  that  may  be  asserted  concerning  the 
numberless  and  very  diverse  events  that  take  place  in  the 
natural  world  around  us.  The  greater  part,  if  not,  as 
some  philosophers  think,  the  whole  of  our  knowledge,  is 
ultimately  due  to  inductive  reasoning.  The  mind,  it  is 
plausibly  said,  is  not  furnished  with  knowledge  in  the 
form  of  general  propositions  ready  made  and  stamped 
upon  it,  but  is  endowed  with  powers  of  observation,  com- 
parison, and  reasoning,  which  are  adequate,  when  well 
educated  and  exercised,  to  procure  knowledge  of  the  world 
without  us  and  the  world  within  the  human  mind.  Even 
when  we  argue  synthetically  and  deductively  from  simple 
ideas  and  truths  which  seem  to  be  ready  in  the  mind,  as 
in  the  case  of  the  science  of  geometry,  it  may  be  that  we 
have  gathered  those  simple  ideas  and  truths  from  previous 
observation  or  induction  of  an  almost  unconscious  kind 
This  is  a  debated  point  upon  which  I  will  not  here  speak 
positively ;  but  if  the  truth  be  as  stated,  Induction  will  be 
the  mode  by  which  all  the  materials  of  knowledge  are 
brought  to  the  mind  and  analysed.  Deduction  wiL  then 
be  the  almost  equally  important  process  by  which  the 
knowledge  thus  acquired  is  utilised,  and  by  which  new 
Inductions  of  a  more  complicated  character,  as  we  shall 
lee,  are  rendered  possible. 

An  Induction,  that  is  an  act  of  Inductive  reasoning,  is 
called  Perfect  when  all  the  possible  cases  or  instances  to 
which  the  conclusion  can  refer,  have  been  examined  and 


THE  INDUCTIVE  SYLLOGISM.          aij 

enumerated  in  the  premises.  If,  as  usually  happens,  it  is 
impossible  to  examine  all  cases,  since  they  may  occur  at 
future  times  or  in  distant  parts  of  the  earth  or  othei 
regions  of  the  universe,  the  Induction  is  called  Imperfect 
The  assertion  that  all  the  months  of  the  year  are  of  less 
length  than  thirty-two  days  is  derived  from  Perfect  In- 
duction, and  is  a  certain  conclusion  because  the  calendar 
is  a  human  institution,  so  that  we  know  beyond  doubt  how 
many  months  there  are,  and  can  readily  ascertain  that 
each  of  them  is  less  than  thirty-two  days  in  length.  But 
the  assertion  that  all  the  planets  move  in  one  direction 
round  the  sun,  from  West  to  East,  is  derived  from  Imper- 
fect Induction ;  for  it  is  possible  that  there  exist  planets 
more  distant  than  the  most  distant-known  planet  Nep- 
tune, and  to  such  a  planet  of  course  the  assertion  would 
apply. 

Hence  it  is  obvious  that  there  is  a  great  difference 
between  Perfect  and  Imperfect  Induction.  The  latter 
includes  some  process  by  which  we  are  enabled  to  make 
assertions  concerning  things  that  we  have  never  seen  or 
examined  or  even  known  to  exist  But  it  must  be  care- 
fully remembered  also  that  no  Imperfect  Induction  can 
give  a  certain  conclusion.  It  may  be  highly  probable  or 
nearly  certain  that  the  cases  unexamined  will  resemble 
those  which  have  been  examined,  but  it  can  never  be 
certain.  It  is  quite  possible,  for  instance,  that  a  new 
planet  might  go  round  the  sun  in  an  opposite  direction  to 
the  other  planets.  In  the  case  of  the  satellites  belonging 
to  the  planets  more  than  one  exception  of  this  kind  has 
been  discovered,  and  mistakes  have  constantly  occurred 
b  science  from  expecting  that  all  new  cases  would 
exactly  resemble  old  ones.  Imperfect  Induction  thui 
gives  only  a  certain  degree  of  probability  or  likelihood 
that  all  instances  will  agree  with  those  examined.  Per- 
fect Induction,  on  the  other,  hand,  gives  a  necessary  and 


BI4  PERFEC1    INDUCTION  AND 

certain   conclusion,  but  it  asserts  nothing  beyond  whai 
«ras  asserted  in  the  premises.  i 

Mr  Mill,  indeed,  differs  from  almost  all  other  logicians 
in  holding  that  Perfect  Induction  is  improperly  called 
Cnduction,  because  it  does  not  lead  to  any  new  knowledge. 
He  defines  Induction  as  inference  from  the  known  to  ttu 
unknown,  and  considers  the  unexamined  cases  which  are 
apparently  brought  into  our  knowledge  as  the  only  gain 
from  the  process  of  reasoning.  Hence  Perfect  Induction 
seems  to  him  to  be  of  no  scientific  value  whatever,  be- 
cause the  conclusion  is  a  mere  reassertion  in  a  briefer 
form,  a  mere  summing  up  of  the  premises.  I  may  point 
out,  however,  that  if  Perfect  Induction  were  no  more  than 
a  process  of  abbreviation  it  is  yet  of  great  importance,  and 
requires  to  be  continually  used  in  science  and  common 
life.  Without  it  we  could  never  make  a  comprehensive 
statement,  but  should  be  obliged  to  enumerate  every  par- 
ticular. After  examining  the  books  in  a  library  and 
finding  them  to  be  all  English  books  we  should  be  unable 
to  sum  up  our  results  in  the  one  proposition,  "all  the  books 
in  this  library  are  English  books  ;"  but  should  be  required 
to  go  over  the  list  of  books  every  time  we  desired  to  make 
any  one  acquainted  with  the  contents  of  the  library.  The 
fact  is,  that  the  power  of  expressing  a  great  number  of 
particular  facts  in  a  very  brief  space  is  essential  to  the  pro- 
gress of  science.  Just  as  the  whole  science  of  arithmetic 
consists  in  nothing  but  a  series  of  processes  for  abbreviat- 
ing addition  and  subtraction,  and  enabling  us  to  deal  with 
a.  great  number  of  units  in  a  very  short  time,  so  Perfect 
Induction  is  absolutely  necessary  to  enable  us  to  deal  with 
ft  great  number  of  particular  facts  in  a  very  brief  space. 

It  is  usual  to  represent  Perfect  Induction  in  the  form 
of  an  Inductive  Syllogism,  as  in  the  following  instance  .•— 
Mercury,  Venus,  the  Earth,  &c.,  all  move  round  the  sue 
from  West  to  East 


xxv.j       THE  INDUCTIVE  SYLLOGISM.         tl» 

Mercury,  Venus,  the  Earth,  &c.,  are  all  the  known  Planet* 
Therefore  all  the  known  planets  move  round  the  sun  from 
West  to  East. 

This  argument  is  a  true  Perfect  Induction  because  the 
conclusion  only  makes  an  assertion  of  all  known  planets 
which  excludes  all  reference  to  possible  future  discoveries 
and  we  may  suppose  that  all  the  known  planets  have  been 
enumerated  in  the  premises.  The  form  of  the  argument 
appears  to  be  that  of  a  syllogism  in  the  third  figure, 
namely  Darapti,  the  middle  term  consisting  in  the  group 
of  the  known  planets.  In  reality,  however,  it  is  not  an 
ordinary  syllogism.  The  minor  premise  states  not  that 
Mercury,  Venus,  the  Earth,  Neptune,  &c.,  are  contained 
among  the  known  planets,  but  that  they  are  those  planets, 
or  are  identical  with  them.  This  premise  is  then  a 
doubly  universal  proposition  of  a  kind  (p.  184 — 7)  not  re- 
cognised in  the  Aristotelian  Syllogism.  Accordingly  we 
may  observe  that  the  conclusion  is  a  universal  proposi- 
tion, which  is  not  allowable  in  the  third  figure  of  the  syl- 
logism. 

As  another  example  of  a  Perfect  Induction  we  may 
take— 

January,  February, December,  each  contain  leit 

than  32  days. 

January December  are  all  the  months  of  the  year. 

Therefore  all  the  months  of  the  year  contain  kss  than  32 
days. 

Although  Sir  W.  Hamilton  has  entirely  rejected  the 
notion,  it  seems  worthy  of  inquiry  whether  the  Inductive 
Syllogism  be  not  really  of  the  Disjunctive  form  of  Sylla 
gism.  Thus  1  should  be  inclined  to  represent  the  last 
example  in  the  form: 

A  month  of  the  year  is  either  January,  or  February, 
M  March —or  December  but  January  has  less 


n6  PERFECT  INDUCTION  AND        [LE8& 

than  32  days ;  and  February  has  less  than  32  days ;  and 
so  on  until  we  come  to  December,  which  has  less  than 
52  days. 

It  follows  clearly  that  a  month  must  in  any  case  have 
less  than  32  days;  for  there  are  only  12  possible  case*, 
tnd  in  each  case  this  is  affirmed.  The  fact  is  that  the 
major  premise  of  the  syllogism  on  the  last  page  is  a 
compound  sentence  with  twelve  subjects,  and  is  therefore 
equivalent  to  twelve  distinct  logical  propositions.  The 
minor  premise  is  either  a  disjunctive  proposition,  as  I  have 
represented  it,  or  something  quite  different  from  anything 
we  have  elsewhere  had. 

From  Perfect  Induction  we  shall  have  to  pass  to  Im- 
perfect Induction ;  but  the  opinions  of  Logicians  are  not 
in  agreement  as  to  the  grounds  upon  which  we  are  war- 
ranted in  taking  a  part  of  the  instances  only,  and  con- 
cluding that  what  is  true  of  those  is  true  of  all.  Thus  if 
we  adopt  the  example  found  in  many  books  and  say— 

This,  that,  and  the  other  magnet  attract  iron ; 
This,  that,  and  the  other  magnet  are  all  magnets ; 
Therefore  all  magnets  attract  iron, 

we  evidently  employ  a  false  minor  premise,  because  this, 
that,  and  the  other  magnet  which  we  have  examined, 
cannot  possibly  be  all  existing  magnets.  In  whatevei 
form  we  put  it  there  must  be  an  assumption  that  the  mag- 
nets which  we  have  examined  are  a  fair  specimen  of  all 
magnets,  so  that  what  we  find  in  some  we  may  expect  in 
ail  Archbishop  Whately  considers  that  this  assumption 
thould  be  expressed  in  one  of  the  premises,  and  he  repre« 
•ents  Induction  as  a  Syllogism  in  Barbara  as  follows : — 
That  which  belongs  to  this,  that,  and  the  other  magnet. 

belongs  to  all ; 

Attracting  iron  belongs  to  this,  that,  and  the  other ; 
Therefore  it  belongs  to  all 


XXV.]       THE  INDUCTIVE  SYLLOGISM  11} 

But  though  this  is  doubtless  a  correct  expression  of  th« 
Assumption  made  in  an  Imperfect  Induction,  it  does  not 
in  the  least  explain  the  grounds  on  which  we  are  allowed 
to  make  the  assumption,  and  under  what  circumstances 
such  an  assumption  would  be  likely  to  prove  true.  Some 
writers  have  asserted  that  there  is  a  Principle  called  the 
Uniformity  of  Nature,  which  enables  us  to  affirm  that 
what  has  often  been  found  to  be  true  of  anything  will 
continue  to  be  found  true  of  the  same  sort  of  thing.  It 
must  be  observed,  however,  that  if  there  be  such  a  principle 
it  is  liable  to  exceptions;  for  many  facts  which  have  held 
true  up  to  a  certain  point  have  afterwards  been  found  not 
to  be  always  true.  Thus  there  was  a  wide  and  unbroken 
induction  tending  to  show  that  all  the  Satellites  in  the 
planetary  system  went  in  one  uniform  direction  round 
their  planets.  Nevertheless  the  Satellites  of  Uranus  when 
discovered  were  found  to  move  in  a  retrograde  direction, 
or  in  an  opposite  direction  to  all  Satellites  previously 
known,  and  the  same  peculiarity  attaches  to  the  Satellite 
of  Neptune  more  lately  discovered. 

We  may  defer  to  the  next  lesson  the  question  of  the 
varying  degree  of  certainty  which  belongs  to  induction  in 
the  several  branches  of  knowledge. 

The  advanced  student  may  consult  the  following  with 
idvantage : — Mansel's  Aldrich,  Appendix,  Notes  G  and  H. 
Hamilton's  Lectures  on  Logic,  Lecture  xvii.,  and  Appen 
dix  VI  I.,  On  Induction  and  Example,  VoL  II.,  p.  358.  J.  S, 
Mill's  System,  of  Logic,  Book  III.  Chap.  2,  Of  Induction* 
improperly  so-t*U*4> 


LESSON   XXVI. 

GEOMETRICAL  AND  MATHEMATICAL  INDUO 
TION,  ANALOGY  AND  EXAMPLE. 

IT  is  now  indispensable  that  we  should  consider  with 
great  care  upon  what  grounds  Imperfect  Induction  is 
founded.  No  difficulty  is  encountered  in  Perfect  Indue 
tion  because  all  possible  cases  which  can  come  under  the 
general  conclusion  are  enumerated  in  the  premises,  so 
that  in  fact  there  is  no  information  in  the  conclusion  which 
was  not  given  in  the  premises.  In  this  respect  the  In- 
ductive Syllogism  perfectly  agrees  with  the  general  prin- 
ciples of  deductive  reasoning,  which  require  that  the  in- 
formation contained  in  the  conclusion  should  be  shown 
only  from  the  data,  and  that  we  should  merely  unfold, 
or  transform  into  an  explicit  statement  what  is  contained 
in  the  premises  implicitly. 

In  Imperfect  Induction  the  process  seems  to  be  of  a 
wholly  different  character,  since  the  instances  concerning 
which  we  acquire  knowledge  may  be  infinitely  more 
numerous  than  those  from  which  we  acquire  the  know- 
ledge. Let  us  consider  in  the  first  place  the  process  of 
Geometrical  Seasoning  which  has  a  close  resemblance  to 
inductive  reasoning.  When  in  the  fifth  proposition  of  the 
first  book  of  Euclid  we  prove  that  the  angles  at  the  base 
of  an  isosceles  triangle  are  equal  to  each  other,  it  is  done 
by  taking  one  particular  triangle  as  an  example.  A 
figure  is  given  which  the  reader  is  requested  to  regard  as 
having  two  equal  sides,  and  it  is  conclusively  proved  thai 
if  the  sides  be  really  equal  then  the  angles  opposite  to 
those  sides  must  be  equal  also.  But  Euclid  says  nothing 
about  other  isosceles  triangles  ;  he  treats  one  single 
triangle  as  a  sufficient  specimen  of  all  isosceles  triangles, 


AND  EXAMPLE.  21* 

and  we  are  asked  to  believe  that  what  is  true  of  that  if 
true  of  any  other,  whether  its  sides  be  so  small  as  to  be 
only  visible  in  a  microscope,  or  so  large  as  to  reach  to  the 
furthest  fixed  star.  There  may  evidently  be  an  infinite 
number  of  isosceles  triangles  as  regards  the  length  of  the 
equal  sides,  and  each  of  these  may  be  infinitely  varied  by 
increasing  or  diminishing  the  contained  angle,  so  that  the 
number  of  possible  isosceles  triangles  is  infinitely  infinite ; 
ind  yet  we  are  asked  to  believe  of  this  incomprehensible 
number  of  objects  what  we  have  proved  only  of  one  single 
specimen.  This  might  seem  to  be  the  most  extremely 
Imperfect  Induction  possible,  and  yet  every  one  allows 
that  it  gives  us  really  certain  knowledge.  We  do  know 
with  as  much  certainty  as  knowledge  can  possess,  that 
if  lines  be  conceived  as  drawn  from  the  earth  to  two  stars 
equally  distant,  they  will  make  equal  angles  with  the  line 
joining  those  stars ;  and  yet  we  can  never  have  tried  the 
experiment 

The  generality  of  this  geometrical  reasoning  evidently 
depends  upon  the  certainty  with  which  we  know  that  all 
isosceles  triangles  exactly  resemble  each  other.  The  pro- 
position proved  does  not  in  fact  apply  to  a  triangle  unless 
it  agrees  with  our  specimen  in  all  the  qualities  essential 
to  the  proof.  The  absolute  length  of  any  of  the  sides  or 
the  absolute  magnitude  of  the  angle  contained  between 
any  of  them  were  not  points  upon  which  the  proof  de- 
pended— they  were  purely  accidental  circumstances ; 
hence  we  are  at  perfect  liberty  to  apply  to  all  new  cases 
of  an  isosceles  triangle  what  we  learn  of  one  case.  Upon 
a  similar  ground  rests  all  the  vast  body  of  certain  know- 
ledge  contained  in  the  mathematical  sciences — not  only 
All  tV  geometrical  truths,  but  all  general  algebraical 
trutlb.  It  was  shown,  for  instance,  in  p.  58,  that  ii 
a  and  b  be  two  quantities,  and  we  multiply  together 
their  sum  and  difference,  we  get  the  difference  of  thf 


tic  INDUCTION,  ANALOGY  [LESA 

squares  of  a  and  b.  However  often  we  try  this  It  will  b< 
found  true  ;  thus  if  a  =  10  and  b  =  7,  the  product  of  tht 
sum  and  difference  is  17  x  3  =  51;  the  squares  of  th> 
quantities  are  10  x  10  or  100  and  7  x  7  or  49,  the  dirfer 
ence  of  which  is  also  51.  But  however  often  we  tried  tbt 
rule  no  certainty  would  be  added  to  it;  because  whei 
proved  algebraically  there  was  no  condition  which  re 
•tricted  the  result  to  any  particular  numbers,  and  a 
and  b  might  consequently  be  any  numbers  whatever 
This  generality  of  algebraical  reasoning  by  which  a  pro- 
perty is  proved  of  infinite  varieties  of  numbers  at  once,  is 
one  of  the  chief  advantages  of  algebra  over  arithmetic 
There  is  also  in  algebra  a  process  called  Mathematical 
Induction  or  Demonstrative  Induction,  which  shows  the 
powers  of  reasoning  in  a  very  conspicuous  way.  A  good 
example  is  found  in  the  following  problem  :—  If  we  take 
the  first  two  consecutive  odd  numbers,  i  and  3,  and  add 
them  together  the  sum  is  4,  or  exactly  twice  two;  if  we 
take  three  such  numbers  1+3  +  5,  the  sum  is  9  or  exactly 
three  times  three;  if  we  take  four,  namely  i  +  3  +  5  +  7  the 
sum  is  1  6,  or  exactly  four  times  four;  or  generally,  if  we 
take  any  given  number  of  the  series,  1+3  +  5  +  7  +  ...  the 
sum  is  equal  to  the  number  of  the  terms  multiplied  by 
itself.  Anyone  who  knows  a  very  little  algebra  can  prove 
that  this  remarkable  law  is  universally  true,  as  follows— 
Let  n  be  the  number  of  terms,  and  assume  for  a  moment 
that  this  law  is  true  up  to  n  terms,  thus  — 

1+3  +  5  +  7  +  ......  +(2»-  1)=«'. 

Now  add  2«  +  1  to  each  side  of  the  equation.    It  fol 
lows  that— 


But  the  last  quantity  *a  +  2«  +  I  is  just  equal  to  (n  +  1)«  . 
10  that  if  the  law  is  true  for  n  terms  it  is  true  also  for  »-*-] 
We  are  enabled  to  areue  from  each  single  case  of 


AND  EXAMPLE.  221 

the  law  to  the  next  case ;  buv  we  have  already  shown  that 
k  is  true  of  the  first  few  cases,  therefore  it  must  be  true  01 
all.  By  no  conceivable  labour  could  a  person  ascertain  by 
trial  what  is  the  sum  of  the  first  billion  odd  numbers,  and 
yet  symbolically  or  by  general  reasoning  we  know  with 
certainty  that  they  would  amount  to  a  billion  billion,  and 
aeither  more  nor  less  even  by  a  unit.  This  process  oi 
Mathematical  Induction  is  not  exactly  the  same  as  Geo- 
metrical Induction,  because  each  case  depends  upon  the 
last,  but  the  proof  rests  upon  an  equally  narrow  basis  of 
experience,  and  creates  knowledge  of  equal  certainty  and 
generality. 

Such  mathematical  truths  depend  upon  observation 
of  a  few  cases,  but  they  acquire  certainty  from  the  per- 
ception we  have  of  the  exact  similarity  of  one  case  to 
another,  so  that  we  undoubtingly  believe  what  is  true  of 
one  case  to  be  true  of  another.  It  is  very  instructive  to 
contrast  with  these  cases  certain  other  ones  where  there 
is  a  like  ground  of  observation,  but  not  the  same  tie  of 
similarity.  It  was  at  one  time  believed  that  if  any  integral 
number  were  multipled  by  itself,  added  to  itself  and  then 
added  to  41,  the  result  would  be  a  prime  number,  that  is 
a  number  which  could  not  be  divided  by  any  other  in 
tegral  number  except  unity ;  in  symbols, 
•**+ .r+4i  =  prime  number. 

This  was  believed  solely  on  the  ground  of  trial  and 
experience,  and  it  certainly  holds  for  a  great  many  values 
of  x.  Thus  when  x  is  successively  made  equal  to  the 
aumbers  in  the  first  line  below,  the  expression  **+  r  +  41 
jures  the  values  in  the  second  line,  and  they  are  all  primf 
ismbers : 

01234$      6      789      10 
4»     43     47     S3    61     71     »3     97     113  «3'   *$' 

No  reason  however  could   be   given   why   it   should 


1*2  INDUCTION,  ANALOGY 

always  be  true,  and  accordingly  it  is  found  that  the  rule 
does  not  always  hold  true,  but  fails  when  x =  40.  Then 
we  have  40x40-1-40  +  41  =  1681,  but  this  is  clearly  equal 
to  41  x  40  +  41  or  41  x  41,  and  is  not  a  prime  number. 

In  that  branch  of  mathematics  which  treats  of  the 
peculiar  properties  and  kinds  of  numbers,  other  proposi- 
tions depending  solely  upon  observation  have  been  as- 
serted to  be  always  true.  Thus  Fermat  believed  that 

• 

2a  4- 1  always  represents  a  prime  number,  but  could  not 
give  any  reason  for  the  assertion.  It  holds  true  in  fact 
until  the  product  reaches  the  large  number  4294967297, 
which  was  found  to  be  divisible  by  641,  so  that  the  gene- 
rality of  the  statement  was  disproved. 

We  find  then  that  in  some  cases  a  single  instance 
proves  a  general  and  certain  rule,  while  in  others  a  very 
great  number  of  instances  are  insufficient  to  give  any 
certainty  at  all;  all  depends  upon  the  perception  we  have 
of  similarity  or  identity  between  one  case  and  another. 
We  can  perceive  no  similarity  between  all  prime  numbers 
which  assures  us  that  because  one  is  represented  by  a 
certain  formula,  also  another  is;  but  we  do  find  such 
similarity  between  the  sums  of  odd  numbers,  or  between 
isosceles  triangles. 

Exactly  similar  considerations  apply  to  inductions  in 
physical  science.  When  a  chemist  analyses  a  few  grains 
of  water  and  finds  that  they  contain  exactly  8  parts  of 
oxygen  and  I  of  hydrogen  for  9  parts  of  water,  he  feels 
warranted  in  asserting  that  the  same  is  true  of  all  pure 
water  whatever  be  its  origin,  and  whatever  be  the  part  of 
the  world  from  which  it  comes.  But  if  he  analyse  a  piece 
of  granite,  or  a  sample  of  sea-water  from  one  part  of  the 
tforld,  he  does  not  feel  any  confidence  that  it  will  resem- 
ble exactly  a  piece  of  granite,  or  a  sample  of  sea-watei 
from  another  part  of  the  earth ;  hence  he  does  not  venture 
to  assert  of  all  granite  or  sea-water,  what  he  finds  true  of 


xxvi.]  AND  EXAMPLE.  i&\ 

•  single  sample.  Extended  experience  shows  that  gra- 
nite is  very  variable  in  composition,  but  that  sea-water  is 
rendered  pretty  uniform  by  constant  mixture  of  currents. 
Nothing  but  experience  in  these  cases  could  inform  us 
how  far  we  may  assert  safely  of  one  sample  what  we  nave 
ascertained  of  another.  But  we  have  reason  to  believe 
that  chemical  compounds  are  naturally  fixed  and  invari- 
able in  composition,  according  to  Dalton's  laws  of  com- 
bining proportions.  No  a  priori  reasoning  from  the 
principles  of  thought  could  have  told  us  this,  and  we  only 
learn  it  by  extended  experiment  But  having  once  shown 
it  to  be  true  with  certain  substances  we  do  not  need  to 
repeat  the  trial  with  all  other  substances,  because  we  have 
every  reason  to  believe  that  it  is  a  natural  law  in  which 
all  chemical  substances  resemble  each  other.  It  is  only 
necessary  then  for  a  single  accurate  analysis  of  a  given 
fixed  compound  to  be  made  in  order  to  inform  us  of  the 
composition  of  all  other  portions  of  the  same  substance. 

It  must  be  carefully  observed  however  that  all  indue, 
UOOB  in  physical  science  are  only  probable,  or  that  if  cer- 
tain, it  is  only  hypothetical  certainty  they  possess.  Can 
I  be  absolutely  certain  that  all  water  contains  one  part 
of  hydrogen  in  nine  ?  I  am  certain  only  on  two  con- 
ditions :— 

1.  That  this  was  certainly  the  composition  of  the 
sample  tried. 

2.  That  any  other   substance   I  call  water  exactly 
resembles  that  sample. 

But  even  if  the  first  condition  be  undoubtedly  true,  I 
cannot  be  certain  of  the  second.  For  how  do  I  know 
what  is  water  except  by  the  fact  of  its  being  a  transparent 
liquid,  freezing  into  a  solid  and  evaporating  into  steam, 
possessing  a  high  specific  heat,  and  a  number  of  other 
distinct  properties  ?  But  can  I  be  absolutely  certain  that 
every  liquid  possessing  all  these  properties  is  water? 


134  INDUCTION,  ANALOGY  [LESi 

Practically  I  can  be  certain,  but  theoretically  I  cannot 
Two  substances  may  have  been  created  so  like  each  ithei 
that  we  should  never  yet  have  discovered  the  difference ; 
we  might  then  be  constantly  misled  by  assuming  of  the 
one  what  is  only  true  of  the  other.  That  this  should  evei 
happen  with  substances  possessing  the  very  distinct  quali 
ties  of  water  is  excessively  improbable,  but  so  far  is  it 
from  being  impossible  or  improbable  in  other  cases,  that 
it  has  often  happened.  Most  of  the  new  elements  dis- 
covered in  late  years  have,  without  doubt,  been  mistaken 
previously  for  other  elements.  Caesium  and  Rubidium 
had  been  long  mistaken  for  each  other,  and  for  Potassium, 
before  they  were  distinguished  by  Bunsen  and  Kirchhofl 
by  means  of  the  spectroscope.  As  they  are  new  known 
to  be  widely  distributed,  although  in  small  quantities,  it  is 
certain  that  what  was  supposed  to  be  Potassium  in  many 
thousands  of  analyses  was  partly  composed  of  different 
substances.  Selenium  had  probably  been  confused  with 
Sulphur,  and  there  are  certain  metals— for  instance,  Rho- 
dium, Ruthenium,  Indium,  Osmium,  and  Beryllium — 
Yttrium,  Erbium,  Cerium,  Lanthanum,  and  Didymium — 
Cadmium  and  Indium — which  have  only  recently  been 
distinguished.  The  progress  of  science  will  doubtless 
show  that  we  are  mistaken  in  many  of  our  identifications, 
and  various  difficulties  thus  arising  will  ultimately  be  ex- 
plained. 

Take  again  a  very  different  case  of  induction.  Are 
we  certain  that  the  sun  will  rise  again  to-morrow  morning 
as  it  has  risen  for  many  thousand  years,  and  probably  f  )i 
some  hundred  million  years?  We  are  certain  only  on  thii 
condition  or  hypothesis,  that  the  planetary  system  proceeds 
to-morrow  as  it  has  proceeded  for  so  long.  Many  causes 
may  exist  which  might  at  any  moment  defeat  all  our 
calculations ;  our  sun  is  believed  to  be  a  variable  star,  and 
for  what  we  know  it  might  at  any  moment  suddenly 


HXVL]  AND  EXAMPLE.  n\ 

explode  or  flare  up,  as  certain  other  stars  have  been  oi> 
served  to  do,  and  we  should  then  be  all  turned  into  thin 
luminous  vapour  in  a  moment  of  time.  It  is  not  at  all 
impossible  that  a  collision  did  once  occur  in  the  planet- 
ary system,  and  that  the  minute  planets  or  asteroids  are 
the  result  Even  if  there  is  no  large  meteor,  comet  or 
sther  body  capable  of  breaking  up  the  earth  by  collision, 
yet  it  is  probable  that  the  sun  moves  through  space  at  the 
rate  of  nearly  300  miles  per  minute,  and  if  some  other 
star  should  meet  us  at  a  similar  rate  the  consequences 
would  be  inconceivably  terrible.  It  is  highly  improbable 
however  that  such  an  event  should  come  to  pass  even  in 
the  course  of  a  million  years. 

The  reader  will  now  see  that  no  mere  Imperfect  In- 
duction can  give  certain  knowledge ;  all  inference  proceeds 
upon  the  assumption  that  new  instances  will  exactly  re- 
semble old  ones  in  all  material  circumstances ;  but  in 
natural  phenomena  this  is  purely  hypothetical,  and  we 
may  constantly  find  ourselves  in  error.  In  Mathematical 
Induction  certainty  arose  from  the  cases  being  hypotheti- 
cal in  their  own  nature,  or  being  made  so  as  exactly  to 
correspond  with  the  conditions.  We  cannot  assert  that 
any  triangle  existing  in  nature  has  two  equal  sides  or  two 
equal  angles,  and  it  is  even  impossible  in  practice  that 
any  two  lines  or  angles  can  be  absolutely  equal.  But  it 
is  nevertheless  true  that  if  the  sides  are  equal  the  angles 
are  equal.  All  certainty  of  inference  is  thus  relative  and 
hypothetical.  Even  in  the  syllogism  the  certainty  of  the 
conclusion  only  rests  on  the  hypothesis  of  certainty  in  the 
premises.  It  is  probable,  in  fact,  that  all  reasoning  reduces 
kself  to  a  single  type — that  what  is  true  of  one  thing  will 
be  true  of  another  thing,  on  condition  of  there  being  an 
exact  resemblance  between  them  in  all  material  circum- 
stances. 

The  reader  will  now  understand  with  ease  the  nature 


aa6  INDUCTION,  ANALOGY  [LISS 

of  reasoning  by  analogy.  In  strictness  an  analogy  is  not 
an  identity  of  one  thing  with  another,  but  an  identity  ol 
relations.  In  the  case  of  numbers  7  is  not  identical  with 
10  nor  14  with  20,  but  the  ratio  of  7  to  10  is  identical  with 
the  ratio  of  14  to  20,  so  that  there  is  an  analogy  between 
these  numbers.  To  multiply  two  by  two  is  not  the  same 
thing  as  to  construct  a  square  upon  a  line  two  units 
long ;  but  there  is  this  analogy — that  there  will  be  just  as 
many  units  of  area  in  the  square  as  there  are  units  in  the 
product  of  two  by  two.  This  analogy  is  so  evident  that 
we  fearlessly  assert  a  square  mile  to  consisi  of  1760  x  1760 
square  yards  without  any  trial  of  the  truth.  In  ordinary 
language,  however,  analogy  has  come  to  mean  any  re- 
semblance between  things  which  enables  us  to  believe  of 
one  what  we  know  of  the  other. 

Thus  the  planet  Mars  possesses  an  atmosphere,  with 
clouds  and  mist  closely  resembling  our  own ;  it  has  seas 
distinguished  from  the  land  by  a  greenish  colour,  and 
polar  regions  covered  with  snow.  The  red  colour  of  tne 
planet  seems  to  be  due  to  the  atmosphere,  like  the  red 
colour  of  our  sunrises  and  sunsets.  So  much  is  similar 
in  the  surface  of  Mars  and  the  surface  of  the  Earth 
that  we  readily  argue  there  must  be  inhabitants  there 
as  here.  All  that  we  can  certainly  say  however  is, 
that  if  the  circumstances  be  really  similar,  and  similar 
germs  of  life  have  been  created  there  as  here,  there  must 
be  inhabitants.  The  fact  that  many  circumstances  are 
similar  increases  the  probability.  But  between  the  Earth 
ind  the  Sun  the  analogy  is  of  a  much  fainter  character ; 
we  speak  indeed  of  the  sun's  atmosphere  being  subject  to 
storms  and  filled  with  clouds,  but  these  clouds  are  heated 
probably  beyond  the  temperature  of  our  hottest  furnaces  ; 
if  they  produce  rain  it  must  resemble  a  shower  of  melted 
iron ;  and  the  sun-spots  are  perturbations  of  so  tremend- 
ous a  sue  and  character,  that  the  earth  together  with 


XXVI.  J  AND  EXAMPLE.  33) 

half-a-dozen  of  the  other  planets  could  readily  be  swal- 
lowed up  in  one  of  them*.  It  is  plain  then  that  there  is 
little  or  no  analogy  between  the  Sun  and  the  Earth,  anc 
we  can  therefore  with  difficulty  form  a  conception  of  any- 
'.hing  going  on  in  a  sun  or  star. 

Argument  from  analogy  may  be  defined  as  direct 
inductive  inference  from  one  instance  to  any  similai 
instance.  It  may,  as  Mr  Mill  says,  be  reduced  to  the 
following  formula : — 

"Two  things  resemble  each  other  in  one  or  mort 
respects ;  a  certain  proposition  is  true  of  the  one ;  there- 
fore it  is  true  of  the  other."  This  is  no  doubt  the  type  o( 
all  reasoning,  and  the  certainty  of  the  process  depends 
entirely  upon  the  degree  of  resemblance  or  identity  be- 
tween the  cases.  In  geometry  the  cases  are  absolutely 
identical  in  all  material  points  by  hypothesis,  and  no 
doubt  attaches  to  the  inference ;  in  physical  science  the 
identity  is  a  question  of  probability,  and  the  conclusion  is 
HI  a  like  degree  probable.  It  should  be  added  that  Mr 
Mill  considers  Geometrical  and  Mathematical  Induction 
not  to  be  properly  called  Induction,  for  reasons  of  which 
the  force  altogether  escapes  my  apprehension  ;  but  the 
reader  will  find  his  opinions  in  the  2nd  chapter  of  the 
3rd  book  of  his  System  of  Logic, 

One  form  of  analogical  or  inductive  argument  consists 
in  the  constant  use  of  examples  and  Instances.  The  best 
way  to  describe  the  nature  of  a  class  of  things  is  to  pie- 
>ent  one  of  the  things  itself,  and  point  out  the  pr<  perties 
which  belong  to  the  class  as  distinguished  from  those 
peculiar  to  the  thing.  Throughout  these  Lessons,  as 
throughout  every  work  on  Logic,  instances  of  propositions, 
of  compound  or  complex  sentences,  of  syllogisms,  &c.5  arc 
continually  used,  and  the  rtader  is  asked  to  apply  to  alJ 

*  Lockyer's  EUmtniary  Lessons  in  Astronomy,  §  108. 

15— a 


128  OB  SEX  VA  T1ON  [] 

similar  cases  what  he  observes  in  the  examples  given 
It  is  assumed  that  the  writer  selects  such  examples  as 
truly  exhibit  the  properties  in  question. 

While  all  inductive  and  analogical  inferences  rest 
upon  the  same  principles  there  are  wide  differences  be- 
tween the  sources  of  probability.  In  analogy  we  have  two 
cases  which  resemble  each  other  in  a  great  many  proper- 
ties, and  we  infer  that  some  additional  property  in  one  is 
probably  to  be  found  ia  the  other.  The  very  narrow 
basis  of  experience  is  compensated  by  the  high  degree  of 
similarity.  In  the  processes  more  commonly  treated 
under  the  name  Induction,  the  things  usually  resemble 
each  other  only  in  two  or  three  properties,  and  we  require 
to  have  more  instances  to  assure  us  that  what  is  true  of 
of  these  is  probably  true  of  all  similar  instances.  The 
less,  in  short,  the  intension  of  the  resemblance  the  greater 
must  be  the  extension  of  our  inquiries. 

We  proceed  to  the  ordinary  processes  of  Induction  in 
the  following  Lessons. 

Mr  Mill's  System  of  Logic,  Book  ill.  Chap.  XX.  Oj 
Analogy.  Mans  el's  Aldruh,  App.  Note  H.  On 
Example  and  Analogy. 


LESSON   XXVII. 

OBSERVATION  AND   EXPERIMENT. 

ALL  knowledge,  it  may  be  safely  said,  must  be  ultimately 
founded  upon  experience,  which  is  but  a  general  name  foi 
the  various  feelings  impressed  upon  the  mind  at  any  period 
of  its  existence.  The  mind  never  creates  entirely  new 
knowledge  independent  of  experience,  and  all  that  th« 
reasoning  powers  can  do  is  to  arrive  at  the  full  meaning 


XXvii.1  AND  EXPERIMENT.  2*3 

of  the  facts  which  are  in  our  possession.  In  previous 
centuries  men  of  the  highest  ability  have  held  that  the 
mind  of  its  own  power  alone  could,  by  sufficient  cogita- 
tion, discover  what  things  outside  us  should  be,  and 
wou.d  be  found  to  be  on  examination.  They  thought 
that  we  were  able  to  anticipate  Nature  by  evolving 
from  the  human  mind  an  idea  of  what  things  would  bt 
made  by  the  Creator.  The  celebrated  philosopher  Des 
cartes  thus  held  that  whatever  the  mind  can  clearl) 
conceive  may  be  considered  true;  but  we  can  conceive 
the  existence  of  mountains  of  gold  or  oceans  of  fresh 
water,  which  do  not  as  a  fact  exist  Anything  that  we 
can  clearly  conceive  must  be  conformable  to  the  laws  oi 
thought,  and  its  existence  is  then  not  impossible,  so  far  as 
our  intellect  is  concerned;  but  the  forms  and  sizes  and 
manners  in  which  it  has  pleased  the  Creator  to  make 
things  in  this  or  any  other  part  of  the  universe,  cannot 
possibly  be  anticipated  by  the  exceedingly  limited  wisdom 
of  the  human  mind,  and  can  only  be  learnt  by  actual  ex- 
amination of  existing  things. 

In  the  latter  part  of  the  I3th  century  the  great  Roger 
Bacon  clearly  taught  in  England  the  supreme  importance 
of  experience  as  the  basis  of  knowledge ;  but  the  same 
doctrine  was  also,  by  a  curious  coincidence,  again  upheld 
in  the  I7th  century  by  the  great  Chancellor  Francis 
Bacon,  after  whom  it  has  been  called  the  Baconian  Phi- 
losophy. I  believe  that  Roger  Bacon  was  even  a  greater 
man  than  Francis,  whose  fame  is  best  known ;  but  the 
words  in  which  Francis  Bacon  proclaimed  the  importance 
of  experience  and  experiment  must  be  ever  memorable. 
In  the  beginning  of  his  great  work,  the  Novum  Organum,  oi 
New  Instrument,  he  thus  points  out  our  proper  position 
as  learners  in  the  world  of  nature. 

"Man,  the  Servant  and  Interpreter  of  Nature,  can  de 
and  understand  as  much  as  he  has  observed  concerning 


t*  OBSERVATION  [LESt, 

the  order  of  nature  in  outward  tilings  or  in  the  mind 
more,  he  can  neither  know  nor  do." 

The  above  is  the  first  of  the  aphorisms  or  paragraph* 
with  which  the  Novum  Organum  commences.  In  the 
second  aphorism  he  asserts  that  the  unaided  mind  car, 
effect  little  and  is  liable  to  err ;  assistance  in  the  form  of 
a  definite  logical  method  is  requisite,  and  this  it  was  the 
purpose  of  his  New  Instrument  to  furnish.  The  3rd  and 
4th  aphorisms  must  be  given  entire ;  they  are : — 

"  Human  science  and  human  power  coincide,  because 
ignorance  of  a  cause  deprives  us  of  the  effect  For  nature 
is  not  conquered  except  by  obedience ;  and  what  we  dis- 
cover as  a  cause  by  contemplation  becomes  a  rule  IE 
operation." 

"Man  can  himself  do  nothing  else  than  move  natural 
bodies  to  or  from  each  other ;  nature  working  within  ac- 
complishes the  rest." 

It  would  be  impossible  more  clearly  and  completely 
to  express  the  way  in  which  we  discover  science  by  inter- 
preting the  changes  we  observe  in  nature,  and  then  turn 
our  knowledge  to  a  useful  purpose  in  the  promotion  of 
the  arts  and  manufactures.  We  cannot  create  and  we 
cannot  destroy  a  particle  of  matter ;  it  is  now  known  that 
we  cannot  even  create  or  destroy  force ;  nor  can  we  really 
alter  the  inner  nature  of  any  substance  that  we  have  to 
deal  with.  All  that  we  can  do  is  to  observe  carefully  how 
one  substance  by  its  natural  powers  acts  upon  another 
substance,  and  then  by  noving  them  together  at  the  right 
time  we  can  effect  our  object;  as  Bacon  says,  "Nature 
working  within  does  the  rest."  Had  it  not  been  the 
nature  of  heat  when  applied  to  water  to  develope  steam 
possessing  elastic  power,  it  is  needless  to  say  that  th« 
steam-engine  could  never  have  been  made,  so  that  the 
invention  of  the  steam-engine  arose  from  observing  the 
utility  of  the  force  of  steam,  and  employing  it  accordingly 


xxvii.  j  AND  EXPERIMENT.  33. 

It  is  in  this  sense  that  Virgil  has  proclaimed  bin  happ) 
who  knows  the  causes  of  things— 

Felix  qui  potuit  rerum  cognosccre  ca*s*st 

and  that  Bacon  has  said,  Knowledge  is  Power.  So  fat 
is  we  have  observed  how  things  happen  in  nature,  and  OB 
arhat  occasion  particular  effects  are  brought  to  pass,  we 
are  enabled  to  avoid  or  utilise  those  effects  as  we  may 
desire,  not  by  altering  the  natures  of  things,  but  by 
allowing  them  in  suitable  times  and  circumstances  to 
manifest  their  own  proper  powers.  It  is  thus,  as  Tenny- 
son has  excellently  said,  that  we 

"  Rule  by  obeying  Nature's  Powers." 

Inductive  logic  treats  of  the  methods  of  reasoning  by 
which  we  may  successfully  interpret  nature  and  learn  the 
natural  laws  which  various  substances  obey  in  different 
circumstances.  In  this  lesson  we  consider  the  first  requi- 
site of  induction,  namely,  the  experience  or  examination 
of  nature  which  is  requisite  to  furnish  us  with  facts.  Such 
experience  is  obtained  either  by  observation  or  experiment. 
To  observe  is  merely  to  notice  events  and  changes  which 
are  produced  in  the  ordinary  course  of  nature,  without 
being  able,  or  at  least  attempting,  to  control  or  vary  those 
changes.  Thus  the  early  astronomers  observed  the  mo- 
tions of  the  sun,  moon  and  planets  among  the  fixed  stars, 
and  gradually  detected  many  of  the  laws  or  periodical 
returns  of  those  bodies.  Thus  it  is  that  the  meteorologist 
observes  the  ever-changing  weather,  and  notes  the  height 
af  the  barometer,  the  temperature  and  moistness  of  the 
lir,  the  direction  and  force  of  the  wind,  the  height  and 
character  of  the  clouds,  without  being  in  the  least  able  to 
govern  any  of  these  facts.  The  geologist  again  is  gene- 
nerally  a  simple  observer  when  he  investigates  the  nature 
and  position  of  rocks.  The  zoologist,  the  botanist,  and 


zj2  OBSER  VA  TION  [LES* 

the  mineralogist  usually  employ  mere  observation  when 
they  examine  animals,  plants,  and  minerals,  as  they  aw 
met  with  in  their  natural  condition. 

In  experiment,  on  the  contrary,  we  vary  at  our  will 
the  combinations  of  things  and  circumstances,  and  then 
observe  the  result.  It  is  thus  that  the  chemist  discovers 
the  composition  of  water  by  using  an  electric  current  to 
separate  its  two  constituents,  oxygen  and  hydrogen.  The 
mineralogist  may  employ  experiment  when  he  melts  twc 
Of  three  substances  together  to  ascertain  how  a  particular 
mineral  may  have  been  produced.  Even  the  botanist  and 
zoologist  are  not  confined  to  passive  observation ;  for  by 
removing  animals  or  plants  to  different  climates  and  dif- 
ferent soils,  and  by  what  is  called  domestication,  they 
may  try  how  far  the  natural  forms  and  species  are  capable 
of  alteration. 

It  is  obvious  that  experiment  is  the  most  potent  and 
direct  mode  of  obtaining  facts  where  it  can  be  applied. 
We  might  have  to  wait  years  or  centuries  to  meet  acci- 
dentally with  facts  which  we  can  readily  produce  at  any 
moment  in  a  laboratory  ;  and  it  is  probable  that  most  of 
the  chemical  substances  now  known,  and  many  exces- 
sively useful  products,  would  never  have  been  discovered 
at  all  by  waiting  till  nature  presented  them  spontaneously 
to  our  observation.  Many  forces  and  changes  too  may 
go  on  in  nature  constantly,  but  in  so  slight  a  degree  as  to 
escape  our  senses,  and  render  some  experimental  means 
necessary  for  their  detection.  Electricity  doubtless  ope- 
rates in  every  particle  of  matter,  perhaps  at  every  mo- 
ment of  time  ;  and  even  the  ancients  could  not  but  notice 
its  action  in  the  loadstone,  in  lightning,  in  the  Aurora 
Borealis,  or  in  a  piece  of  rubbed  amber  (electrum).  But 
in  lightning  electricity  was  too  intense  and  dangerous; 
in  the  other  cases  it  was  too  feeble  to  be  properly  under- 
stood. The  science  of  electricity  and  magnetism  could 


KXVIL]  AND  EXPERIMENT.  233 

only  advance  by  getting  regular  supplies  of  electricity 
from  the  common  electric  machine  or  the  galvanic  bat- 
tery, and  by  making  powerful  electro-magnets.  Most  i) 
not  all  the  effects  which  electricity  produces  must  go  on  in 
nature,  but  altogether  too  obscurely  for  observation. 

Experiment,  again,  is  rendered  indispensable  by  the 
fact  that  on  the  surface  of  the  earth  we  usually  meet  sub- 
stances under  certain  uniform  conditions,  so  that  we 
could  never  learn  by  observation  what  would  be  the 
nature  of  such  substances  under  other  conditions.  Thus 
carbonic  acid  is  only  met  in  the  form  of  a  gas,  proceeding 
from  the  combustion  of  carbon  ;  but  when  exposed  to 
extreme  pressure  and  cold,  it  is  condensed  into  a  liquid, 
and  may  even  be  converted  into  a  snow-like  solid  sub- 
stance. Many  other  gases  have  in  like  manner  been 
liquefied  or  solidified ;  and  there  is  reason  to  believe  that 
every  substance  is  capable  of  taking  all  the  three  forms  of 
solid,  liquid  and  gas,  if  only  the  conditions  of  temperature 
and  pressure  can  be  sufficiently  varied.  Mere  observation 
of  nature  would  have  led  us,  on  the  contrary,  to  suppose 
that  nearly  all  substances  were  fixed  in  one  condition 
only,  and  could  not  be  converted  from  solid  into  liquid 
and  from  liquid  into  gas. 

It  must  not  be  supposed  however  that  we  can  draw 
any  precise  line  between  observation  and  experiment,  and 
say  where  the  one  ends  and  the  other  begins.  The  dif- 
ference is  rather  one  of  degree  than  of  kind;  and  all  we 
can  say  is  that  the  more  we  vary  the  conditions  artificially 
the  more  we  employ  experiment.  I  have  said  that  me- 
teorology is  a  science  of  nearly  pure  observation,  but  if  we 
purposely  ascend  mountains  to  observe  the  rarefaction 
and  cooling  of  the  atmosphere  by  elevation,  or  if  we  make 
balloon  ascents  for  the  same  purpose,  like  Gay  Lussac 
and  Glaisher,  we  so  vary  the  mode  of  observation  as 
almost  to  render  it  experimental.  Astronomers  again 


a  34  OBSER  VA  TION 

may  almost  be  said  to  experiment  instead  of  merely  ob- 
serving when  they  simultaneously  employ  instruments  ai 
far  to  the  north,  and  as  far  to  the  south,  upon  the  earth's 
surface  as  possible,  in  order  to  observe  the  apparent  dif- 
ference of  place  of  Venus  when  crossing  the  sun  in  a 
transit,  so  as  thus  to  compare  the  distances  of  Venus  and 
the  sun  with  the  dimensions  of  the  earth. 

Sir  John  Herschel  has  excellently  described  the  dif 
ference  in  question  in  his  Discourse  on  the  Study  of  Na- 
tural Philosophy*.  "  Essentially  they  are  much  alike, 
and  differ  rather  in  degree  than  in  kind ;  so  that  perhaps 
the  terms  passive  and  active  observation  might  bettei 
express  their  distinction;  but  it  is,  nevertheless,  highly 
important  to  mark  the  different  states  of  mind  in  inqui- 
ries carried  on  by  their  respective  aids,  as  well  as  their 
different  effects  in  promoting  the  progress  of  science. 
In  the  former,  we  sit  still  and  listen  to  a  tale,  told  us,  per- 
haps obscurely,  piecemeal,  and  at  long  intervals  of  time, 
with  our  attention  more  or  less  awake.  It  is  only  by  after 
rumination  that  we  gather  its  full  import ;  and  often,  when 
the  opportunity  is  gone  by,  we  have  to  regret  that  our 
attention  was  not  more  particularly  directed  to  some  point 
which,  at  the  time,  appeared  of  little  moment,  but  of 
which  we  at  length  appreciate  the  importance.  In  the 
latter,  on  the  other  hand,  we  cross-examine  our  witness, 
and  by  comparing  one  part  of  his  evidence  with  the  other, 
while  he  is  yet  before  us,  and  reasoning  upon  it  in  his 
presence,  are  enabled  to  put  pointed  and  searching  ques- 
tions, the  answer  to  which  may  at  once  enable  us  to  make 
up  our  minds.  Accordingly  it  has  been  found  invariably, 
that  in  those  departments  of  physics  where  the  pheno- 
mena are  beyond  our  control,  or  into  which  experimental 
enquiry,  from  other  causes,  has  not  been  carried,  th*  pro 


XXVIL]  AND  EXPERIMENT.  23i 

gress  of  knowledge  has  been  slow,  uncertain  and  irregu, 
lar ;  while  in  such  as  admit  of  experiment,  and  in  which 
mankind  have  agreed  to  its  adoption,  it  has  been  rapid 
sure,  and  steady." 

Not  uncommonly,  however,  nature  has,  so  to  speak 
made  experiments  upon  a  scale  and  for  a  duration  witk 
which  we  cannot  possibly  compete.  Thus  we  do  not  need 
to  try  the  soil  and  situation  which  suits  any  given  plant 
best ;  we  have  but  to  look  about  and  notice  the  habitat  01 
situation  in  which  it  is  naturally  found  in  the  most  flou- 
rishing condition,  and  that,  we  may  be  sure,  indicates  the 
result  of  ages  of  natural  experiment.  The  distances  oi 
the  fixed  stars  would  probably  have  been  for  ever  un- 
known to  us  did  not  the  earth  by  describing  an  orbit  with 
a  diameter  of  182,000,000  miles  make  a  sort  of  experimen- 
tal base  for  observation,  so  that  we  can  see  the  stars  in 
very  slightly  altered  positions,  and  thus  judge  their  dis- 
tances compared  with  the  earth's  orbit*.  Eclipses,  tran- 
sits, occultations  and  remarkable  conjunctures  of  the  pla- 
nets, are  also  kinds  of  natural  experiments  which  have 
often  been  recorded  in  early  times,  and  thus  afford  data 
of  the  utmost  value. 

Logic  can  give  little  or  no  aid  in  making  an  acute  or 
accurate  observer.  There  are  no  definite  rules  which  can 
be  laid  down  upon  the  subject.  To  observe  well  is  an  art 
which  can  only  be  acquired  by  practice  and  training ;  and 
it  is  one  of  the  greatest  advantages  of  the  pursuit  of  the 
Natural  Sciences  that  the  faculty  of  clear  and  steady  ob- 
servation is  thereby  cultivated.  Logic  can  however  give 
us  this  caution,  which  has  been  well  pointed  out  by  Mr 
Mill — to  discriminate  accurately  between  what  we  really 
do  observe  and  what  we  only  infer  from  the  facts  observed. 
So  long  as  we  only  record  and  describe  what  our  sensei 

•  See  Lockyer't  Elementary  Leuons  in  Astronomy,  Not 
XLVI,  XLVII. 


*3<>  OBSERVATION  [LESS 

have  actually  witnessed,  we  cannot  commit  an  error ;  but 
the  moment  we  presume  or  infer  anything  we  are  liable  tc 
mistake.  For  instance,  we  examine  the  sun's  surface 
with  a  telescope  and  observe  that  it  is  intensely  bright 
except  where  there  are  small  breaks  or  circular  openings 
in  the  surface  with  a  dark  interior.  We  are  irresistibly 
led  to  the  conclusion  that  the  inside  of  the  sun  is  colder 
and  darker  than  the  outside,  and  record  as  a  fact  that  we 
saw  the  dark  interior  of  the  sun  through  certain  openings 
in  its  luminous  atmosphere.  Such  a  record,  however, 
would  involve  mistaken  inference,  for  we  saw  nothing  but 
dark  spots,  and  we  should  not  have  done  more  in  observ- 
ation than  record  the  shape,  size,  appearance  and  change 
of  such  spots.  Whether  they  are  dark  clouds  above  the 
luminous  surface,  glimpses  of  the  dark  interior,  or,  as  is 
now  almost  certainly  inferred,  something  entirely  different 
from  either,  can  only  be  proved  by  a  comparison  of  many 
unprejudiced  observations. 

The  reader  cannot  too  often  bear  in  mind  the  cau- 
tion against  confusing  facts  observed  with  inferences  from 
those  facts.  It  is  not  too  much  to  say  that  nine-tenths  of 
what  we  seem  to  see  and  hear  is  inferred,  not  really  felt 
Every  sense  possesses  what  are  called  acquired  percep- 
tions, that  is,  the  power  of  judging  unconsciously,  by  long 
experience,  of  many  things  which  cannot  be  the  objects  oi 
direct  perception.  The  eye  cannot  see  distance,  yet  we 
constantly  imagine  and  say  that  we  see  things  at  such 
and  such  distances,  unconscious  that  it  is  the  result  of 
judgment.  As  Mr  Mill  remarks,  it  is  too  much  to  say 
"  I  saw  my  brother."  All  I  positively  know  is  that  I 
saw  some  one  who  closely  resembled  my  brother  as  fat 
as  could  be  observed  It  is  by  judgment  only  I  can 
assert  he  was  my  brother,  and  that  judgment  may  possi- 
Dly  be  wrong. 

Nothing  is  more  important  in  observation  and  expert 


xxvii.]  AND  EXPERIMENT.  j# 

ment  than  to  be  uninfluenced  by  any  prejudice  or  theory 
in  correctly  recording  the  facts  observed  and  allowing  to 
them  their  proper  weight.  He  who  does  not  do  so  will 
almost  always  be  able  to  obtain  facts  in  support  of  an 
opinion  however  erroneous.  Thus  the  belief  still  existi 
with  great  force  in  the  majority  of  uneducated  persons, 
that  the  moon  has  great  influence  over  the  weather.  The 
changes  of  the  moon,  full,  new  and  half  moon,  occur  four 
times  in  every  month,  and  it  is  supposed  that  any  change 
may  influence  the  weather  at  least  on  the  day  preceding 
or  following  that  of  its  occurrence.  There  will  thus  be 
twelve  days  out  of  every  28  on  which  any  change  of  wea- 
ther would  be  attributed  to  the  moon,  so  that  during  the 
jear  many  changes  will  probably  be  thus  recorded  as 
favourable  to  the  opinion.  The  uneducated  observer  is 
struck  with  these  instances  and  remembers  them  care- 
fully, but  he  fails  to  observe,  or  at  least  to  remember,  that 
changes  of  weather  often  occur  also  when  there  is  no 
change  of  the  moon  at  all  The  question  could  only 
be  decided  by  a  long  course  of  careful  and  unbiassed 
observation  in  which  all  facts  favourable  or  unfavour- 
able should  be  equally  recorded.  All  observations  which 
have  been  published  negative  the  idea  that  there  can  be 
any  such  influence  as  the  vulgar  mind  attributes  to  the 
moon. 

But  it  would  at  the  same  time  be  an  error  to  suppose 
that  the  best  observer  or  experimentalist  is  he  who  holds 
no  previous  opinions  or  theories  on  the  subject  he  inves- 
tigates. On  the  contrary,  the  great  experimentalist  is  he 
who  ever  has  a  theory  or  even  a  crowd  of  theories  or  ideas 
upon  his  mind,  but  is  always  putting  them  to  the  test  of 
experience  and  dismissing  those  which  are  false.  The 
number  of  things  which  can  be  observed  and  experimented 
on  are  infinite,  and  if  we  merely  set  to  work  to  record 
facts  without  any  distinct  purpose,  our  records  will  havf 


138  OBSERVATION.  frv. 

no  value.  We  must  have  some  opinion  cr  some  the- 
ory to  direct  our  choice  of  experiments,  and  it  is  more 
probable  that  we  hit  upon  the  truth  in  this  way  than 
merely  by  haphazard.  But  the  great  requisite  of  the 
true  philosopher  is  that  he  be  perfectly  unbiassed  and 
abandon  every  opinion  as  soon  as  facts  inconsistent  with 
it  are  observed. 

It  has  been  well  said  by  the  celebrated  Turgot,  that 
"  the  first  thing  is  to  invent  a  system ;  the  second  thing 
is  to  be  disgusted  with  it;"  that  is  to  say,  we  ought  to 
have  some  idea  of  the  truth  we  seek,  but  should  im- 
mediately put  it  to  a  severe  trial  as  if  we  were  inclined  to 
distrust  and  dislike  it  rather  than  be  biassed  in  its  favour. 
Few  men  probably  have  entertained  more  false  theories 
than  Kepler  and  Faraday ;  few  men  have  discovered  or 
established  truths  of  greater  certainty  and  importance. 
Faraday  has  himself  said  that — 

"  The  world  Httle  knows  how  many  of  the  thoughts 
and  theories  which  have  passed  through  the  mind  of  a 
scientific  investigator,  have  been  crushed  in  silence  and 
secrecy  by  his  own  severe  criticism  and  adverse  examina- 
tion ;  that  in  the  most  successful  instances  not  a  tenth  of 
the  suggestions,  the  hopes,  the  wishes,  the  preliminary 
tonclusions  have  been  realized  *." 

The  student  is  strongly  recommended  to  read  Sir 
J.  Herschel's  Preliminary  Discourse  on  the  Stud) 
if  Natural  Philosophy  (Lardner's  Cabinet  Cycle- 
padia\  especially  Part  II.  Chaps.  4  to  7,  concerning 
Observation,  Experiment,  and  the  Inductive  Pro 
cesses  generally. 

•  AMtrn  Cultttrt,  edited  by  Yoram,  p.  *««.     [M*cmiUM 


KXY1U.]  METHODS  OF  INDUCTION 


LESSON   XXVIII. 
METHODS  OF  INDUCTION. 

WE  have  now  to  consider  such  methods  as  can  be  laid! 
down  for  the  purpose  of  guiding  us  in  the  search  for  gene- 
ral truths  or  laws  of  nature  among  the  facts  obtained  by 
observation  and  experiment.  Induction  consists  in  infer- 
ring from  particulars  to  generals,  or  detecting  a  general 
truth  among  its  particular  occurrences.  But  in  physical 
science  the  truths  to  be  discovered  generally  relate  to 
the  connection  of  cause  and  effect,  and  we  usually  caU 
them  laws  of  causation  or  natural  laws.  By  the  Gam*  of 
an  event  we  mean  the  circumstances  which  must  have 
preceded  in  order  that  the  event  should  happen,  Nor  is 
it  generally  possible  to  say  that  an  event  has  one  single 
cause  and  no  more.  There  are  usually  many  different 
things,  conditions  or  circumstances  necessary  to  the  pro- 
duction of  an  effect,  and  all  of  them  must  be  considered 
causes  or  necessary  parts  of  the  cause.  Thus  the  cause 
of  the  loud  explosion  in  a  gun  is  not  simply  the  pulling  of 
the  triggei,  which  is  only  the  last  apparent  cause  or 
jocaslon  of  the  explosion ;  the  qualities  of  the  powder; 
the  proper  form  of  the  barrel ;  the  existence  of  some  re- 
sisting charge ;  the  proper  arrangement  of  the  percussion 
cap  and  powder ;  the  existence  of  a  surrounding  atmo- 
sphere, are  among  the  circumstances  necessary  to  the 
loud  report  of  a  gun :  any  of  them  being  absent  it  would 
not  have  occurred. 

The  cause  of  the  boiling  of  water  again  is  not  merely 
the  application  of  heat  up  to  a  certain  degree  of  tempera- 


MO  METHODS  OF  INDUCTION. 

ture,  but  the  possibility  also  of  the  escape  of  the  vapour 
when  it  acquires  a  certain  pressure.  The  freezing  ol 
water  similarly  does  not  depend  merely  upon  the  with 
drawal  of  heat  below  the  temperature  of  o°  Centigrade. 
It  is  the  work  of  Induction  then  to  detect  those  circum- 
stances which  uniformly  will  produce  any  given  effect  • 
and  as  soon  as  these  circumstances  become  known,  we 
have  a  law  or  uniformity  of  nature  of  greater  or  less  gene- 
rality. 

In  this  and  the  following  Lessons  I  shall  often  have  tc 
use,  in  addition  to  cause  and  effect,  the  words  antecedent 
and  consequent,  and  the  reader  ought  to  notice  their 
meanings.  By  an  antecedent  we  mean  any  thing,  condi- 
tion, or  circumstance  which  exists  before  or,  it  may  be,  at 
the  same  time  with  an  event  or  phenomenon.  By  a  con- 
sequent we  mean  any  thing,  or  circumstance,  event,  or 
phenomenon,  which  is  different  from  any  of  the  antecedents 
and  follows  after  their  conjunction  or  putting  together. 
It  does  not  follow  that  an  antecedent  is  a  cause,  because 
the  effect  might  have  happened  without  it.  Thus  the 
sun's  light  may  be  an  antecedent  to  the  burning  of  a 
house,  but  not  the  cause,  because  the  house  would  burn 
equally  well  in  the  night  A  necessary  or  indispensabU 
antecedent  is  however  identical  with  a  cause,  being  thai 
without  which  the  effect  would  not  take  place. 

The  word  phenomenon  will  also  be  often  used.  It 
means  simply  anything  which  appears,  and  is  therefore 
observed  by  the  senses ;  the  derivation  of  the  word  from 
the  Greek  word  Qaivoprvov,  that  which  appears,  exactly 
corresponds  to  its  logical  use. 

The  first  method  of  Induction  is  that  which  Mr  Mill 
has  aptly  called  the  Method  of  agreement.  It  depends 
upon  the  rule  that  "If  two  or  more  instances  of  the  phe- 
nomenon under  investigation  have  only  one  circumstance 
in  common,  the  circumstance  in  which  alone  all  the  in- 


*X/m.]     METHODS  OF  INDUCTION.  341 

stances  agree,  is  the  cause  (or  effect)  of  the  given  pheno 
menon."  The  meaning  of  this  First  Canon  of  inductive 
inquiry  might,  I  think,  be  more  briefly  expressed  by  saying 
that  the  sole  invariable  antecedent  of  a  phenomenon  it 
probably  its  cause. 

To  apply  this  method  we  must  collect  as  many  in- 
stances of  the  phenomenon  as  possible,  and  compare 
together  their  antecedents.  Among  these  the  causes  will 
lie,  but  if  we  notice  that  certain  antecedents  are  present  or 
absent  without  appearing  to  affect  the  result,  we  conclude 
that  they  cannot  be  necessary  antecedents.  Hence  it 
is  the  one  antecedent  or  group  of  antecedents  always 
present,  when  the  effect  follows,  that  we  consider  the  cause. 
For  example,  bright  prismatic  colours  are  seen  on  bub- 
bles, on  films  of  tar  floating  upon  water,  on  thin  plates 
of  .mica,  as  also  on  cracks  in  glass,  or  between  two  pieces 
of  glass  pressed  together.  On  examining  all  such  cases 
they  seem  to  agree  in  nothing  but  the  presence  of  a  very 
thin  layer  or  plate,  and  it  appears  to  make  no  appreciable 
difference  of  what  kind  of  matter,  solid,  liquid,  or  gaseous, 
the  plate  is  made.  Hence  we  conclude  that  such  colours 
are  caused  merely  by  the  thinness  of  the  plates,  and  this 
conclusion  is  proved  true  by  the  theory  of  the  interference 
of  light.  Sir  David  Brewster  beautifully  proved  in  a 
similar  way  that  the  colours  seen  upon  Mother-of-pearl 
are  not  caused  by  the  nature  of  the  substance,  but  by  the 
form  of  the  surface.  He  took  impressions  of  the  Mother- 
•>f-pearl  in  wax,  and  found  that  although  the  substance 
was  entirely  different  the  colours  were  exactly  the  same. 
And  it  was  afterwards  found  that  if  a  plate  of  metal  had 
a  surface  marked  by  very  fine  close  grooves,  it  would  havt 
iridescent  colours  like  those  of  Mother-of-pearl.  Henoe 
it  is  evident  that  the  form  of  the  surface,  which  it  th« 
only  invariable  antecedent  or  condition  requisite  for  thi 
production  of  the  colours,  must  be  their  cause 

ID 


JA2  METHODS  OF  INDUCTION.         [] 

The  method  of  agreement  is  subject  to  a  serious 
difficulty,  called  by  Mr  Mill  the  Plurality  of  C&mea,  con- 
sisting in  the  fact  that  the  same  effect  may  in  different 
instances  be  owing  to  different  causes.  Thus  if  we  in- 
quire accurately  into  the  cause  of  heat  we  find  that  it  is 
produced  by  friction,  by  burning  or  combustion,  by  elec- 
tricity, by  pressure,  &c. ;  so  that  it  does  not  follow  that  il 
there  happened  to  be  one  and  the  same  thing  present  in 
all  the  cases  we  examined  this  would  be  the  cause.  The 
second  method  of  induction  which  we  will  now  consider 
is  free  from  this  difficulty,  and  is  known  as  the  Method  of 
Difference.  It  is  stated  in  Mr  Mill's  Second  Canon  as 
follows  :— 

"  If  an  instance  in  which  the  phenomenon  under  inves- 
tigation occurs,  and  an  instance  in  which  it  does  not 
occur,  have  every  circumstance  in  common  save  one,  that 
one  occurring  only  in  the  former;  the  circumstance  in 
which  alone  the  two  instances  differ,  is  the  effect,  or  the 
cause,  or  an  indispensable  part  of  the  cause,  of  the  phe- 
nomenon." 

In  other  words,  we  may  say  that  the  antecedent  which 
is  invariably  present  when  the  phenomenon  follows,  and 
invariably  absent  when  it  is  absent,  other  circumstance! 
remaining  the  same,  is  the  cause  of  the  phenomenon  in 
those  circumstances. 

Thus  we  can  clearly  prove  that  friction  is  om  cause  of 
heat,  because  when  two  sticks  are  rubbed  together  they 
become  heated;  when  not  rubbed  they  do  not  become 
heated.  Sir  Humphry  Davy  showed  that  even  two  pieces 
of  ice  when  rubbed  together  in  a  vacuum  produce  heat 
as  shown  by  their  melting,  and  thus  completely  demon 
strated  that  the  friction  is  the  source  and  cause  of  the 
heat.  We  prove  that  air  is  the  cause  of  sound  being 
communicated  to  our  ears  by  striking  a  bell  in  the  re* 
ceirtr  of  an  air-pump,  as  Hawksbee  first  did  in  1705,  and 


xxvmj     METHODS  OF  INDUCTION.  143 

then  observing  that  when  the  receiver  is  full  of  air  w* 
hear  the  bell ;  when  it  contains  little  or  no  air  we  do 
not  hear  the  bell.  We  learn  that  sodium  or  any  of  its 
compounds  produces  a  spectrum  having  a  bright  yellow 
double  line  by  noticing  that  there  is  no  such  line  in  the 
spectrum  of  light  when  sodium  is  not  present,  but  that  il 
the  smallest  quantity  of  sodium  be  thrown  into  the  flame 
or  other  source  of  light,  the  bright  yellow  line  instantly 
appears.  Oxygen  is  the  cause  of  respiration  and  life, 
because  if  an  animal  be  put  into  a  jar  full  of  atmospheric 
ah*,  from  vw-hich  the  oxygen  has  been  withdrawn,  it  soon 
becomes  suffocated. 

This  is  essentially  the  great  method  of  experiment 
and  its  utility  mainly  depends  upon  the  precaution  of  only 
varying  one  circumstance  at  a  time,  all  other  circuit* 
stances  being  maintained  just  as  they  were.  This  if 
expressed  in  one  of  the  rules  for  conducting  experiments 
given  by  Thomson  and  Tait  in  their  great  treatise  on 
Natural  Philosophy,  Vol.  I.  p.  307,  as  follows:— 

"  In  all  cases  when  a  particular  agent  or  cause  is  to 
be  studied,  experiments  should  be  arranged  in  such  a  way 
as  to  lead  if  possible  to  results  depending  on  it  alone ;  or, 
if  this  cannot  be  done,  they  should  be  arranged  so  as  to 
increase  the  effects  due  to  the  cause  to  be  studied  til] 
these  so  far  exceed  the  unavoidable  concomitants,  that 
the  latter  maybe  considered  as  only  disturbing,  not  essen- 
tially modifying  the  effects  of  the  principal  agent" 

It  would  be  an  imperfect  and  unsatisfactory  experi- 
ment to  take  air  of  which  the  oxygen  has  been  converted 
into  carbonic  acid  by  the  burning  of  carbon,  and  argue 
that,  because  an  animal  dies  in  such  air,  oxygen  is  the 
cause  of  respiration  Instead  of  merely  withdrawing  the 
oxygen  we  have  a  new  substance,  carbonic  acid,  present, 
which  is  quite  capable  of  killing  the  animal  by  its  own 
poisonous  properties.  The  animal  in  fact  would  be  suffo 

16— 2 


144  METHODS  OF  INDUCTION.         [Lisa, 

cated  even  when  a  considerable  proportion  of  oxygen 
remained,  so  that  the  presence  of  the  carbonic  acid  is  a 
disturbing  circumstance  which  confuses  and  vitiates  the 
-xperiment 

It  is  possible  to  prove  the  existence,  and  even  to  mea- 
sure the  amount  of  the  force  of  gravity,  by  delicately  sus- 
pending a  small  ball  about  the  size  of  a  marble  and  then 
suddenly  bringing  a  very  heavy  leaden  ball  weighing  a 
ton  or  more  close  to  it  The  small  ball  will  be  attracted 
and  set  in  motion;  but  the  experiment  would  not  be  of  the 
least  value  unless  performed  with  the  utmost  precaution. 
It  is  obvious  that  the  sudden  motion  of  the  large  leaden 
ball  would  disturb  the  air,  shake  the  room,  cause  currents 
in  the  air  by  its  coldness  or  warmth,  and  even  occasion 
electric  attractions  or  repulsions;  and  these  would  pro- 
bably disturb  the  small  ball  far  more  than  the  force  of 
gravitation. 

Beautiful  instances  of  experiment  according  to  this 
method  are  to  be  found,  as  Sir  John  Herschel  has  pointed 
out,  in  the  researches  by  which  Dr  Wells  discovered  the 
cause  of  dew.  If  on  a  clear  calm  night  a  sheet  or  othei 
covering  be  stretched  a  foot  or  two  above  the  earth,  so 
as  to  screen  the  ground  below  from  the  open  sky,  dew  will 
be. found  on  the  grass  around  the  screen  but  not  beneath 
it  As  the  temperature  and  moistness  of  the  air,  and  other 
circumstances,  are  exactly  the  same,  the  open  sky  must 
be  an  indispensable  antecedent  to  dew.  The  same  expe- 
riment is  indeed  tried  for  us  by  nature,  for  if  we  make 
observations  of  dew  during  two  nights  which  differ  in  no- 
thing but  the  absence  of  clouds  in  one  and  their  presence 
in  the  other,  we  shall  find  that  the  clear  open  sky  is  requi- 
site to  the  formation  of  dew. 

It  may  often  happen  that  we  cannot  apply  the  method 
of  difference  perfectly  by  varying  only  one  circumstance 
it  a  time.  Thus  we  cannot,  generally  speaking,  try  the 


METHODS  OF  INDUCTION  145 

qualities  of  the  same  substance  in  the  solid  and  liquid 
condition  without  any  other  change  of  circumstances,  be- 
cause it  is  necessary  to  alter  the  temperature  of  the  sub- 
stance in  order  to  liquefy  or  solidify  it  The  temperature 
might  thus  be  the  cause  of  what  we  attribute  to  the  liquid 
or  solid  condition.  Under  such  circumstances  we  have 
to  resort  to  what  Mr  Mill  calls  the  Joint  method  of  agree- 
ment  and  difference,  which  consists  in  a  double  applica- 
tion of  the  method  of  agreement,  first  to  a  number  of 
instances  where  an  effect  is  produced,  and  secondly,  to  a 
number  of  quite  different  instances  where  the  effect  is  not 
produced.  It  is  clearly  to  be  understood,  however,  that 
the  negative  instances  differ  in  several  circumstances 
from  the  positive  ones ;  for  if  they  differed  only  in  one 
circumstance  we  might  apply  the  simple  method  of  differ- 
ence. Iceland  spar,  for  instance,  has  a  curious  power  of 
rendering  things  seen  through  it  apparently  double.  This 
phenomenon,  called  double  refraction,  also  belongs  to 
many  other  crystals ;  and  we  might  at  once  prove  it  to  be 
due  to  crystalline  structure  could  we  obtain  any  transpa- 
rent substance  crystallized  and  uncrystallized,  but  subject 
to  no  other  alteration.  We  have,  however,  a  pretty  satis- 
factory proof  by  observing  that  uniform  transparent  un- 
crystallized substances  agree  in  not  possessing  double 
refraction,  and  that  crystalline  substances,  on  the  other 
hand,  with  certain  exceptions  which  are  easily  explained, 
agree  in  possessing  the  power  in  question.  The  principle 
of  the  Joint  method  may  be  stated  in  the  following  rule, 
which  is  Mr  Mill's  Third  Canon : — 

"If  two  or  more  instances  in  which  the  phenomenon 
occurs  have  only  one  circumstance  in  common,  while  two 
or  more  instances  in  which  it  does  not  occur  have  nothing 
in  common  save  the  absence  of  that  circumstance ;  the 
circumstance  in  which  alone  the  two  sets  of  instances 
(always  or  invariably)  differ,  is  the  effect,  or  the  cause 


246  METHODS  OF  INDUCTION.         [LESS 

or  an  indispensable   part  of  the  cause,  of  the  pheno 
menon." 

I  have  inserted  the  words  in  parentheses,  as  without 
them  the  canon  seems  to  me  to  express  exactly  the  oppo- 
site of  what  Mr  Mill  intends. 

It  may  facilitate  the  exact  comprehension  of  these  m 
dwctive  methods  if  I  give  the  following  symbolic  repre- 
sentation of  them  in  the  manner  adopted  by  Mr  Mill 
Let  A,  B,  C,  D,  E^  &c.,  be  antecedents  which  may  b€ 
variously  combined,  and  let  a,  6,  cy  d,  e,  &c.,  be  effects 
following  from  them.  If  then  we  can  collect  the  following 
sets  of  antecedents  and  effects — 

Antecedents.  Consequents. 

ABC  *bc 

ADE  tuU 

AFG  *fg 

AHK  akk 


we  may  apply  the  method  of  agreement,  and  little  doubt 
will  remain  that  A,  the  sole  invariable  antecedent,  is  the 
ause  of  a. 

The  method  of  difference  is  sufficiently  represented  by—- 
Antecedents. Consequents. 
ABC  abc 
BC  be 

Here  while  B  and  C  remain  perfectly  unaltered  we  find 
that  the  presence  or  absence  of  A  occasions  the  presence 
or  absence  of  a,  of  which  it  is  therefore  the  cause,  in  the 
presence  of  B  and  C.  But  the  reader  may  be  cautioned 
against  thinking  that  this  proves  A  to  be  the  cause  of  a 
under  all  circumstances  whatever. 

Tie  Joint  method  of  agreement  and  difference  is  similars 
represented  bv — 


JLXVIII.J     METHODS  OF  INDUCTION.  349 

Antecedents.  Consequents. 

ABC  abc 

ADE  <uU 


AFG 
AHK 


off 
«** 


R  r* 

TV  t* 

XY  xy 

Here  the  presence  of  A  is  followed  as  in  the  simple  method 
of  agreement  by  a  ;  and  the  absence  of  A,  in  circumstances 
differing  from  the  previous  ones,  is  followed  by  the  ab- 
sence of  a.  Hence  there  is  a  very  high  probability  that 
A  is  the  cause  of  a.  But  it  will  easily  be  seen  that  A  is 
not  the  only  circumstance  in  which  the  two  sets  of  in- 
stances differ,  otherwise  to  any  pair  we  might  apply  the 
simple  method  of  difference.  But  the  presence  of  A  is  a 
circumstance  in  which  one  set  invariably,  or  uniformly, 
or  always,  differs,  from  the  other  set.  This  joint  method  is 
thus  a  substitute  for  the  simpler  method  of  difference  in 
cases  where  that  cannot  be  properly  brought  into  action. 

HerscheFs  Discourse,  part  II.  chap.  6,  p.  144. 

Mill's  System  of  Logic,  book  ill.  chaps.  8  and  9. 


LESSON   XXIX. 
METHODS    OF    QUANTITATIVE    INDUCTION 

THE  methods  of  Induction  described  in  the  last  Lesson 
related  merely  to  the  happening  or  not  happening  of  th« 
event,  the  cause  of  which  was  sought.  Thus  we  learnt 
that  friction  was  one  cause  of  heat  by  observing  that  two 


«*8  METHODS  OF  [LESS 

solid  bodies,  even  two  pieces  of  ice,  rubbed  together,  pro- 
duced heat,  but  that  when  they  were  not  rubbed  there 
was  no  such  production  of  heat.  This,  however,  is  a  very 
elementary  sort  of  experiment ;  and  in  the  progress  of  ac 
investigation  we  always  require  to  measure  the  exact 
luantlty  of  an  effect,  if  it  be  capable  of  being  more  or 
ess,  and  connecting  it  with  the  quantity  of  the  cause. 
There  is  in  fact  a  natural  course  of  progress  through 
which  we  proceed  in  every  such  inquiry,  as  may  be  stated 
in  the  following  series  of  questions. 

I.    Does  the  antecedent  invariably  produce  an  effect? 

a.     In  what  direction  is  that  effect? 

3.  How  much  is  that  effect  in  proportion  to  the  cause? 

4.  Is  it  uniformly  in  that  proportion? 

5.  If  not,  according  to  what  law  does  it  vary? 

Take  for  instance  the  effect  of  heat  in  altering  the 
dimensions  of  bodies.  The  first  question  is,  whether  the 
heating  of  a  solid  body,  say  a  bar  of  iron,  alters  its  length  ; 
the  simple  method  of  difference  enables  us  to  answer  that 
it  does.  The  next  inquiry  shows  that  almost  all  sub- 
stances are  lengthened  or  increased  in  dimensions  by 
heat,  but  that  a  very  few,  such  as  india  rubber,  and  water 
below  4*08°  Cent,  are  decreased.  We  next  ascertain  the 
proportion  of  the  change  to  each  degree  of  temperature, 
which  is  called  the  coefficient  of  expansion.  Thus  iron 
expands  o'oocoi22  of  its  own  length  for  every  i'  Centi- 
grade between  o°  and  100°. 

Still  more  minute  inquiry  shows,  however,  that  the 
expansion  is  not  uniformly  proportional  to  temperature; 
most  metals  expand  more  and  more  rapidly  the  hotter 
they  are,  but  the  details  of  the  subject  need  not  be  con- 
sidered here. 

The  fixed  stars,  again,  have  often  been  mentioned  in 
tLcie  Lessons,  but  the  reader  is  probably  aware  that  they 
me  not  really  fixed.  Taking  any  particular  star,  the 


XXIX.]       QUANTITATIVE  INDUCTION.  249 

astronomer  has  really  to  answer  the  several  five  question* 
stated  below. 

Firstly.     Does  the  star  move  ? 

2ndly.     In  what  direction  does  it  move? 

3rdly.    How  much  does  it  move  in  a  year  or  a  century  I 

4thly.     Does  it  move  uniformly? 

5thly.  If  not,  according  to  what  law  does  the  motion 
vary  in  direction  and  rapidity  ? 

Every  science  and  every  question  in  science  is  first  a 
matter  of  fact  only,  then  a  matter  of  quantity,  and  by 
degrees  becomes  more  and  more  precisely  quantitative. 
Thirty  years  ago  most  of  the  phenomena  of  electricity  and 
electro-magnetism  were  known  merely  as  facts ;  now  they 
can  be  for  the  most  part  exactly  measured  and  calculated. 

As  soon  as  phenomena  can  thus  be  measured  we 
can  apply  a  further  Method  of  Induction  of  a  very  im- 
portant character.  It  is  the  Method  of  Difference  indeed 
applied  under  far  more  favourable  circumstances,  where 
every  degree  and  quantity  of  a  phenomenon  gives  us 
a  new  experiment  and  proof  of  connection  between  cause 
and  effect.  It  may  be  called  the  MetHod  of  Concomitant 
Variations,  and  is  thus  stated  by  Mr  Mill,  in  what  he 
entitles  the  Fifth  Canon  of  Induction : 

"Whatever  phenomenon  varies  in  any  manner  when- 
ever another  phenomenon  varies  in  some  particular  man- 
ner, is  either  a  caust  or  an  effect  of  that  phenomenon,  01 
is  connected  with  it  through  some  fact  of  causation." 

Sir  John  Herschel's  statement  of  the  same  method  if 
as  follows : — "  Increase  or  diminution  of  the  effect,  with  the 
increased  or  diminished  intensity  of  the  cause,  in  casej 
which  admit  of  increase  and  diminution,"  to  which  be 
adds,  "  Reversal  of  the  effect  with  that  of  the  cause." 

The  illustrations  of  this  method  are  infinitely  nu- 
merous. Thus  Mr  Joule,  of  Manchester,  conclusive!) 
proved  that  friction  is  a  cause  of  heat  by  expending  exaol 


150  METHODS  OF  [LES& 

quantities  of  force  in  rubbing  one  substance  against 
another,  and  showed  that  the  heat  produced  was  exactly 
greater  or  less  in  proportion  as  the  force  was  greater  01 
less.  We  can  apply  the  method  to  many  cases  which 
had  previously  been  treated  by  the  simple  method  of  dif- 
ference; thus  instead  of  striking  a  bell  in  a  complete 
vacuum  we  can  strike  it  with  a  very  little  air  in  the 
receiver  of  the  air-pump,  and  we  then  hear  a  very  faint 
sound,  which  increases  or  decreases  every  time  we  in- 
crease or  decrease  the  density  of  the  air.  This  experi- 
ment conclusively  satisfies  any  person  that  air  is  the  cause 
of  the  transmission  of  sound. 

It  is  this  method  which  often  enables  us  to  detect  the 
material  connection  which  exists  between  two  bodies. 
For  a  long  time  it  had  been  doubtful  whether  the  red 
flames  seen  in  total  eclipses  of  the  sun  belonged  to  the 
sun  or  the  moon  ;  but  during  the  last  eclipse  of  the  sun 
it  was  noticed  that  the  flames  moved  with  the  sun,  and 
were  gradually  covered  and  uncovered  by  the  moon  at 
successive  instants  of  the  eclipse.  No  one  could  doubt 
thenceforth  that  they  belonged  to  the  sun. 

Whenever,  again,  phenomena  go  through  Periodic 
Changes,  alternately  increasing  and  decreasing,  we  should 
seek  for  other  phenomena  which  go  through  changes  in 
exactly  the  same  periods,  and  there  will  probably  be  a 
connection  of  cause  and  effect.  It  is  thus  that  the  tides 
are  proved  to  be  due  to  the  attraction  of  the  moon  and 
sun,  because  the  periods  of  high  and  low,  spring  and 
neap  tides,  succeed  each  other  in  intervals  corresponding 
to  the  apparent  revolutions  of  those  bodies  round  th« 
earth.  The  fact  that  the  moon  revolves  upon  its  own 
axis  in  exactly  the  same  period  that  it  revolves  round  th« 
earth,  so  that  for  unknown  ages  past  the  same  side  of  the 
aioon  has  always  been  turned  towards  the  earth,  is  a  most 
jerfect  case  of  concomitant  variations,  conclusively  pror- 


AXIX.J      QUANTITATIVE  INDUCTION.  2? 

ing  that  the  earth's  attraction  governs  the  motion*  of  thi 
moon  on  its  own  axis. 

The  most  extraordinary  case  of  variations  howeva 
Consists  in  the  connection  which  has  of  late  years  been 
shown  to  exist  between  the  Aurora  Borealis,  magnetic 
storms,  and  the  spots  on  the  sun.  It  has  only  in  the 
last  30  or  40  years  become  known  that  the  magnetic 
compass  needle  is  subject  at  intervals  to  very  slight  bu< 
curious  movements  •  and  that  at  the  same  time  there  are 
usually  natural  currents  of  electricity  produced  in  tele- 
graph-wires so  a?  to  interfere  with  the  transmission  of  mes- 
sages. These  disturbances  are  known  as  magnetic  storms, 
and  are  often  observed  to  occur  when  a  fine  display  of 
the  Northern  or  Southern  Lights  is  taking  place  in  some 
part  of  the  earth.  Observations  during  many  years  have 
shown  that  these  storms  come  to  their  worst  at  the  end  of 
every  eleven  years,  the  maximum  taking  place  about  the 
present  year  1870,  and  then  diminish  in  intensity  until 
the  next  period  of  eleven  years  has  passed.  Close  obser- 
vations of  the  sun  during  30  or  40  years  have  shown  that 
the  size  and  number  of  the  dark  spots,  which  are  gigantic 
storms  going  on  upon  the  sun's  surface,  increase  and 
decrease  exactly  at  the  same  periods  of  time  as  the  mag- 
netic storms  upon  the  earth's  surface.  No  one  can  doubt, 
then,  that  these  strange  phenomena  are  connected  to« 
gcther,  though  the  mode  of  the  connection  is  quite  un- 
known. It  is  now  believed  that  the  planets  Jupiter, 
Saturn,  Venus  and  Mars,  are  the  real  causes  of  the  dis- 
turbances; for  Balfour  Stewart  and  Warren  de  la  Rue 
have  shown  that  an  exact  correspondence  exists  between 
the  motions  of  these  planets  and  the  periods  of  the  sun- 
spots.  This  is  a  most  remarkable  and  extensive  case  of 
concomitant  variations. 

We  have  now  to  consider  a  method  of  Induction 
Which  must  be  employed  when  several  causes  act  at  one* 


252  METHODS  OF 

and  their  effects  are  all  blended  together,  producing  • 
Joint  effect  of  the  same  kind  as  the  separate  effects.  % 
in  one  experiment  friction,  combustion,  compression  ai,. 
electric  action  are  all  going  on  at  once,  each  of  thes< 
causes  will  produce  quantities  of  heat  which  will  be  addec 
together,  and  it  will  be  difficult  or  impossible  to  say  ho* 
much  is  due  to  each  cause  separately.  We  may  call  thij 
a  case  of  the  homogeneous  intermixture  of  effects,  the  name 
indicating  that  the  joint  effect  is  of  the  same  kind  as 
the  separate  effects.  It  is  distinguished  by  Mr  Mill  from 
cases  of  the  heterogeneous,  or,  as  he  says,  the  ketero- 
pathic  intermixture  of  effects,  where  the  joint  effect  is 
totally  different  in  kind  from  the  separate  effects.  Thus 
if  we  bend  a  bow  too  much  it  breaks  instead  of  bending 
further ;  if  we  warm  ice  it  soon  ceases  to  rise  in  tempera- 
ture and  melts ;  if  we  warm  water  it  rises  in  temperature 
Homogeneously  for  a  time  but  then  suddenly  ceases,  and 
an  effect  of  a  totally  different  kind,  the  production  of 
vapour,  or  possibly  an  explosion,  follows. 

Now  when  the  joint  effect  is  of  a  heterogeneous  kind 
the  method  of  difference  is  sufficient  to  ascertain  the  cause 
of  its  occurrence.  Whether  a  bow  or  a  spring  will  break 
with  a  given  weight  may  easily  be  tried,  and  whether 
water  will  boil  at  a  given  temperature  in  any  given  state 
f  the  barometer  may  also  be  easily  ascertained.  But  in 
the  homogeneous  intermixture  of  effects  we  have  a  more 
complicated  task.  There  are  several  causes  each  pro- 
ducing a  part  of  the  effect,  and  we  want  to  know  how 
much  is  due  to  each.  In  this  case  we  must  employ  a 
further  Inductive  Method,  called  by  Mr  Mill  the  Method 
of  Residues,  and  thus  stated  in  his  Fourth  Canon  :— 

"  Subduct  from  any  phenomenon  such  part  as  is  known 
by  previous  inductions  to  be  the  effect  of  certain  antece- 
dents, and  the  residue  of  the  phenomenon  is  the  effect  o/ 
the  remaining  antecedents.* 


xxix.]      QUANTITATIVE  INDUCTION.  253 

If  we  know  that  tfce  joint  effect  a,  b,  c  is  due  to  the 
causes  A,  B,  and  C,  and  can  prove  that  a  is  due  to  A  and 
b  to  B,  it  follows  that  c  must  be  due  to  C.  There  cannot 
be  a  simpler  case  of  this  than  ascertaining  the  exact 
weight  of  any  commodity  in  a  cart  by  weighing  the  cart 
and  load,  and  then  subtracting  the  tare  or  weight  of  the 
cart  alone,  which  had  been  previously  ascertained.  We 
can  thus  too  ascertain  how  much  of  the  spring  tides  is 
due  to  the  attraction  of  the  sun,  provided  we  have  pre- 
viously determined  the  height  of  the  tide  due  to  the  moon, 
which  will  be  about  the  average  height  of  the  tides  during 
the  whole  lunar  month.  Then  subtracting  the  moon's 
tide  the  remainder  is  the  sun's  tide. 

Newton  employed  this  method  in  a  beautiful  experi- 
ment to  determine  the  elasticity  of  substances  by  allow- 
ing balls  made  of  the  substances  to  swing  against  each 
other,  and  then  observing  how  far  they  rebounded  com- 
pared with  their  original  fall.  But  the  loss  of  motion  is 
due  partly  to  imperfect  elasticity  and  partly  to  the  resist- 
ance of  the  air.  He  determined  the  amount  of  the  latter 
effect  in  the  simplest  manner  by  allowing  the  balls  to 
swing  without  striking  each  other,  and  observing  how 
much  each  vibration  was  less  than  the  last.  In  this  way 
he  was  enabled  easily  to  calculate  the  quantity  that  must 
be  subtracted  for  the  resistance  of  the  air. 

It  is  this  method  that  we  employ  in  making  allowance 
for  the  errors  or  necessary  corrections  in  observations. 
Few  thermometers  are  quite  correct ;  but  if  we  put  a  ther- 
mometer into  melting  snow,  which  has  exactly  the  tem- 
perature of  o°  Centigrade,  or  32°  Fahr.,  we  can  observe 
exactly  how  much  below  or  above  the  true  point  the 
mercury  stands,  and  this  will  indicate  how  much  we 
ought  to  add  or  subtract  from  readings  of  the  thermometer 
to  make  them  correct.  The  height  of  the  barometer  is 
affected  by  several  causes  besides  the  variation  of  the 


254  METHODS  OF 

pressure  of  the  air.  It  is  decreased  by  the_  capillary 
repulsion  oetween  the  glass  tube  and  the  mercury ;  it  is 
increased  by  the  expansion  of  the  mercury  by  heat,  if  the 
tempeiature  be  above  32°  Fahr. ;  and  it  may  be  increased 
or  decreased  by  any  error  in  the  length  of  the  measure 
employed  to  determine  the  height  In  an  accurate  obser- 
vation all  these  effects  are  calculated  and  allowed  for  in 
the  final  result 

In  chemical  analysis  this  method  is  constantly  em- 
ployed to  determine  the  proportional  weight  of  substances 
which  combine  together.  Thus  the  composition  of  water 
is  ascertained  by  taking  a  known  weight  of  oxide  of 
copper,  passing  hydrogen  over  it  in  a  heated  tube,  and 
condensing  the  water  produced  in  a  tube  containing  sul- 
phuric acid.  If  we  subtract  the  original  weight  of  the 
condensing  tube  from  its  final  weight  we  learn  how  much 
water  is  produced;  the  quantity  of  oxygen  in  it  is  found 
by  subtracting  the  final  weight  of  the  oxide  of  copper 
from  its  original  weight.  If  we  then  subtract  the  weight 
of  the  oxygen  from  that  of  the  water  we  learn  the  weight 
of  the  hydrogen,  which  we  have  combined  with  the  oxygen. 
When  the  experiment  is  very  carefully  performed,  as  de- 
scribed in  Dr  Roscoe's  Lessons  in  Elementary  Chemistry^ 
(P-  38),  we  find  that  88*89  parts  by  weight  of  oxygen  unite 
with  i  ri  i  parts  of  hydrogen  to  form  100  parts  of  water. 

In  all  sciences  which  allow  of  measurement  of  quan- 
tities this  method  is  employed,  but  more  especially  in 
astronomy,  the  most  exact  of  all  the  sciences.  Almost  all 
the  causes  and  effects  in  astronomy  have  been  found  out 
as  residual  phenomena,  that  is,  by  calculating  the  effects  of 
all  known  attractions  upon  a  planet  or  satellite,  and  then 
Dbserving  how  far  it  is  from  the  place  thus  predicted 
When  this  was  very  carefully  done  in  the  case  of  Uranus, 
it  was  still  found  that  the  planet  was  sometimes  before 
and  sometimes  behind  its  true  place.  This  residual  effect 


XXIX.]      QUANTITATIVE   INDUCTION.  a§4 

pointed  to  the  existence  of  some  cause  of  attraction  no* 
then  known,  but  which  was  in  consequence  soon  dis 
covered  in  the  shape  of  the  planet  Neptune.  The  motions 
of  several  comets  have  in  this  way  been  calculated,  but  h 
is  observed  that  they  return  each  time  a  little  later  than 
they  ought.  This  retardation  points  to  the  existence  oi 
w>me  obstructive  power  in  the  space  passed  through,  the 
nature  of  which  is  not  yet  understood. 

Mill's  System  of  Logic,  Book  in.  Chap.  10,  Oftiu. 
Plurality  of  Causes;  a*d  of  the  Intermixture  oj 
Effects. 


LESSON    XXX. 
EMPIRICAL   \ND   DEDUCTIVE   METHODS. 

WE  have  hitherto  treated  of  Deduction  and  Induction  as 
•I  they  were  entirely  separate  and  independent  methods. 
In  reality  they  are  frequently  blended  or  employed  alter- 
nately in  the  pursuit  of  truth ;  and  it  may  be  said  that  all 
the  more  important  and  extensive  investigations  of  science 
rely  upon  one  as  much  as  upon  the  other.  It  is  probably 
the  greatest  merit  in  Mr  Mill's  logical  writings  that  he 
points  out  the  entire  insufficiency  of  what  is  called  the 
Baconian  Method  to  detect  the  more  obscure  and  difficult 
Laws  of  nature.  Bacon  advised  that  we  should  always 
begin  by  collecting  facts,  classifying  them  according  to 
their  agreement  and  difference,  and  gradually  gathering 
*rom  them  laws  of  greater  and  greater  generality.  He 
protested  altogether  against  "anticipating  nature, "that is 
forming  our  own  hypotheses  and  theories  as  to  what  the 
laws  of  nature  probably  are,  and  he  seemed  to  think  that 
systematic  arrangement  of  facts  would  take  the  place  of 


l£6        EMPIRICAL  AND  DEDUCTIVE       juts* 

all  other  methods.    The  reader  will  soon  see  that  the 
progress  of  Science  has  not  confirmed  his  opinions. 

When  a  law  of  nature  is  ascertained  purely  by  induc- 
tion from  certain  observations  or  experiments,  and  has  no 
other  guarantee  for  its  truth,  it  is  said  to  be  an  empirical 
law.  As  Mr  Mill  says,  "Scientific  inquirers  give  the  name 
of  Empirical  Laws  to  uniformities  which  observation  01 
experiment  has  shown  to  exist,  but  on  which  they  hesitate 
to  rely  in  cases  varying  much  from  those  which  have  been 
actually  observed,  for  want  of  seeing  any  reason  why 
such  a  law  should  exist"  The  name  is  derived  from  the 
Greek  word  efwmpio,  meaning  experience  or  trial  In- 
stances of  such  laws  are  abundant  We  learn  empiri- 
cally that  a  certain  strong  yellow  colour  at  sunset,  or  an 
unusual  clearness  in  the  air,  portends  rain ;  that  a  quick 
pulse  indicates  fever;  that  horned  animals  are  always 
ruminants;  that  quinine  affects  beneficially  the  nervous 
system  and  the  health  of  the  body  generally ;  that  strych- 
nine has  a  terrible  effect  of  the  opposite  nature :  all  these 
are  known  to  be  true  by  repeated  observation,  but  we  can 
give  no  other  reason  for  their  being  true,  that  is,  we 
cannot  bring  them  into  harmony  with  any  other  scientific 
facts ;  nor  could  we  at  all  have  deduced  them  or  antici- 
pated them  on  the  ground  of  previous  knowledge.  The 
connection  between  the  sun's  spots,  magnetic  storms, 
auroras,  and  the  motions  of  the  planets  mentioned  in  the 
last  Lesson,  is  perhaps  the  most  remarkable  known 
instance  of  an  empirical  induction ;  for  no  hint  has  yet 
been  given  of  the  way  in  which  these  magnetic  influences 
are  exerted  throughout  the  vast  dimensions  of  the  planet- 
ary system.  The  qualities  of  the  several  alloys  of  metals 
are  also  good  instances  of  empirical  knowledge.  No 
one  can  tell  before  mixing  two  or  three  metals  for  the 
first  time  in  any  given  proportions  what  the  qualities  of 
the  mixture  will  be — that  brass  should  be  both  harder 


xxx.]  METHODS.  257 

and  more  ductile  than  either  of  its  constituents,  copper 
and  zinc ;  that  copper  alloyed  with  the  very  soft  metal  tin 
should  make  hard  and  sonorous  bell-metal ;  that  a  certain 
mixture  of  lead,  bismuth,  tin  and  cadmium,  should  melt 
with  a  temperature  (65°  cent.)  far  below  that  of  boiling 
water*. 

However  useful  may  be  empirical  knowledge,  it  is  yet 
of  slight  importance  compared  with  the  well-connected 
and  perfectly  explained  body  of  knowledge  which  con- 
stitutes an  advanced  and  deductive  science.  It  is  in 
fact  in  proportion  as  a  science  becomes  deductive,  and 
enables  us  to  grasp  more  and  more  apparently  uncon- 
nected facts  under  the  same  law,  that  it  becomes  perfect. 
He  who  knows  exactly  why  a  thing  happens,  will  also 
know  exactly  in  what  cases  it  will  happen,  and  what  dif- 
ference in  the  circumstances  will  prevent  the  event  from 
happening.  Take  for  instance  the  simple  effect  of  hot 
water  in  cracking  glass.  This  is  usually  learnt  empiri- 
cally. Most  people  have  a  confused  idea  that  hot  water 
has  a  natural  and  inevitable  tendency  to  break  glass,  and 
that  thin  glass,  being  more  fragile  than  other  glass,  will  be 
more  easily  broken  by  hot  water.  Physical  science,  how- 
ever, gives  a  very  clear  reason  for  the  effect,  by  showing 
that  it  is  only  one  case  of  the  general  tendency  of  heat  to 
expand  substances.  The  crack  is  caused  by  the  success- 
ful effort  of  the  heated  glass  to  expand  in  spite  of  the 
colder  glass  with  which  it  is  connected.  But  then  we 
shall  see  at  once  that  the  same  will  not  be  true  of  thin 
glass  vessels ;  the  heat  will  pass  so  quickly  through  that 
the  glass  will  be  nearly  equally  heated ;  and  accordingly 
chemists  habitually  use  thin  uniform  glass  vessels  to  hold 
or  boil  hot  liquids  without  fear  of  the  fractures  which  would 
be  sure  to  take  place  in  thick  glass  vessels  or  bottles. 

The  history  of  science  would  show  conclusively  that 
*  Roscoe's  Lessons  in  Elementary  Chemistry,  p.  175. 


j$8          EMPIRICAL  AND  DEDUCTIVE     [L 

deduction  was  the  clue  to  all  the  greatest  discoveries, 
Newton,  after  Galileo  the  chief  founder  of  experimen- 
tal philosophy,  possessed  beyond  all  question  the  great- 
est power  of  deductive  thought  which  has  ever  been 
enjoyed  by  man.  It  is  striking  indeed  to  Compare  his 
results  in  optics  with  those  in  chemistry  or  alchemy.  It 
is  not  generally  known  that  Newton  was  really  an  alche- 
mist, and  spent  days  and  nights  in  constant  experiments 
in  his  laboratory,  trying  to  discover  the  secret  by  which 
metals  could  be  transmuted  into  gold.  But  in  these  re- 
searches all  was  purely  empirical,  and  he  had  no  clue  to 
guide  him  to  successful  experiments.  A  few  happy 
guesses  given  in  his  celebrated  Queries  are  all  the  result 
of  this  labour.  But  in  the  science  of  Optics  it  was  quite 
otherwise ;  here  he  grasped  general  laws,  and  every  ex- 
periment only  led  him  to  devise  and  anticipate  the  results 
of  several  others,  each  more  beautiful  than  the  lost.  Thus 
he  was  enabled  to  establish  beyond  all  doubt  the  founda- 
tions of  the  science  of  the  Spectrum,  now  bearing  such 
wonderful  results.  Some  persons  may  suppose  that 
Newton,  living  shortly  after  Bacon,  adopted  the  Baconian 
method,  but  I  believe  that  there  is  no  reference  to  Bacon 
in  Newton's  works;  and  it  is  certain  that  he  did  not 
employ  the  method  of  Bacon.  The  Prineipia,  though 
containing  constant  appeals  to  experiment  and  observa- 
tion, is  nevertheless  the  result  of  a  constant  and  sustained 
effort  of  deductive  mathematical  reasoning. 

What  Mr  Mill  has  called  the  Deductive  Method,  but 
which  I  think  might  be  more  appropriately  called  the 
3omblned  or  Complete  Method,  consists  in  the  alternate 
use  of  induction  and  deduction.  It  may  be  said  to  have 
three  steps,  as  follows : — 

1.  Direct  Induction. 

2.  Deduction,  or,  as  Mr  Mill  calls  it,  Ratiocination, 
5.    Verification. 


XXX.  J  METHODS.  349 

The  first  process  consists  in  such  a  rough  and  simpU 
appeal  to  experience  as  may  give  us  a  glimpse  of  the  lawi 
which  operate,  without  being  sufficient  to  establish  theii 
truth.  Assuming  them  as  provisionally  true,  we  then 
proceed  to  argue  to  their  effects  in  other  cases,  and  a 
further  appeal  to  experience  either  verifies  or  negatives 
the  truth  of  the  laws  assumed.  There  are,  in  short,  two 
appeals  to  experience  connected  by  the  kitermediate  us« 
of  reasoning.  Newton,  for  instance,  having  passed  a  ray 
of  sun-light  through  a  glass  prism  found  that  it  was  spread 
out  into  a  series  of  colours  resembling  those  of  the  rainbow. 
He  adopted  the  theory  that  white  light  was  actually  com- 
posed of  a  mixture  of  different  coloured  lights,  which 
became  separated  in  passing  through  the  prism.  He  saw 
that  if  this  were  true,  and  he  were  to  pass  an  isolated  ray 
of  the  spectrum,  for  instance,  the  yellow  ray,  through  a 
second  prism,  it  ought  not  to  be  again  broken  up  into 
different  colours,  but  should  remain  yellow  whatever  was 
afterwards  done  with  it.  On  trial  he  found  this  to  be  the 
case,  and  afterwards  devised  a  succession  of  similar  con- 
firmatory experiments  which  verified  his  theory  beyond  all 
possible  doubt. 

It  was  no  mere  accident  that  led  Pascal  to  have  a 
barometer  carried  up  to  the  top  of  the  mountain  Puy  dc 
Dome  in  France.  Galileo,  indeed,  became  acquainted  by 
accident  with  the  fact  that  water  will  not  rise  in  an  ordi- 
nary pump  more  than  33  feet,  and  was  thus  led  to  assert 
that  the  limited  weight  of  the  atmosphere  caused  it  to 
rise.  Torricelli,  reasoning  from  this  theory,  saw  that 
mercury,  which  is  fourteen  times  as  heavy  as  water, 
should  not  rise  more  than  one -fourteenth  part  of  the  dis- 
ance,  or  about  29  or  30  inches.  The  experiment  being 
tried  verified  the  theory.  It  was  the  genius  of  Pascal, 
however,  which  saw  that  the  experiment  required  to  b« 
raried  in  another  way  by  carrying  the  mercurial  barome 

17—3 


jto        EMPIRICAL  AND  DEDUCTIVE      [LESS 

ter  to  the  top  of  a  mountain.  If  the  weight  of  the  atmo 
sphere  were  really  the  cause  of  the  suspension  of  the  mer- 
cury, it  ought  to  stand  lowei  on  the  mountain  than  below, 
because  only  the  higher  parts  of  the  atmosphere  pressed 
upon  the  mountain.  The  success  of  the  experiment  com 
pletely  verified  the  original  hypothesis.  The  progress  ol 
the  experimental  sciences  mainly  depends  upon  the  mod* 
in  which  one  experiment  thus  leads  to  othen,  and  dis- 
closes new  facts,  which  would  in  all  probability  have  nevei 
come  under  our  notice  had  we  confined  ourselves  to  the 
purely  Baconian  method  of  collecting  the  facts  first  and 
performing  induction  afterwards. 

The  greatest  result  of  the  deductive  method  is  no  less 
than  the  theory  of  gravitation,  which  makes  a  perfect 
instance  of  its  procedure.  In  this  case  the  preliminary 
induction  consisted,  we  may  suppose,  in  the  celebrated 
fall  of  the  apple,  which  occurred  while  Newton  was  sitting 
in  an  orchard  during  his  retirement  from  London,  on 
account  of  the  Great  Plague.  The  fall  of  the  apple,  we 
are  told,  led  Newton  to  reflect  that  there  must  be  a  power 
tending  to  draw  bodies  towards  the  earth,  and  he  asked 
himself  the  question  why  the  moon  did  not  on  that  account 
fall  upon  the  earth.  The  Lancashire  astronomer  Horrocks 
suggested  to  his  mind  another  fact,  namely,  that  when  a 
stone  is  whirled  round  attached  to  a  string,  it  exerts  a 
force  upon  the  string,  often  called  centrifugal  force.  Hor- 
rocks remarked  that  the  planets  in  revolving  round  the 
sun  must  tend  in  a  similar  way  to  fly  off  from  the  centre 
Newton  was  acquainted  with  Horrocks'  views,  and  was 
thus  possibly  led  to  suppose  that  the  earth's  attractive 
force  might  exactly  neutralise  the  moon's  centrifugal 
tendency,  so  as  to  maintain  that  satellite  in  constant 
rotation. 

But  it  happened  that  the  world  was  in  possession  ol 
certain  empirical  laws  concerning  the  motions  of  the  pi* 


xxx.]  METHODS.  jfa 

nets,  without  which  Newton  could  scarcely  have  proceeded 
further.  Kepler  had  passed  a  lifetime  in  observing  the 
Heavenly  bodies,  and  forming  hypotheses  to  explain  their 
motions.  In  general  his  ideas  were  wild  and  unfounded, 
but  the  labours  of  a  lifetime  were  rewarded  in  the  esta- 
blishment of  the  three  laws  which  bear  his  name,  and 
describe  the  nature  of  the  orbits  traversed  by  the  planets, 
and  the  relation  between  the  size  of  such  orbit  and.  the 
time  required  by  the  planet  to  traverse  it.  Newton  wai 
able  to  show  by  geometrical  reasoning  that  if  one  body 
revolved  round  another  attracted  towards  it  by  a  force 
decreasing  as  the  square  of  the  distance  increases,  it  would 
necessarily  describe  an  orbit  of  which  Kepler's  laws  would 
be  true,  and  which  would  therefore  exactly  resemble  the 
orbits  of  the  planets.  Here  was  a  partial  verification  of 
his  theory  by  appeal  to  the  results  of  experience.  But 
several  other  philosophers  had  gone  so  far  in  the  investi- 
gation of  the  subject  It  is  Newton's  chief  claim  to  ho- 
nour, that  he  carried  on  his  deductions  and  verifications 
until  he  attained  complete  demonstration.  To  do  this  it 
was  necessary  first  of  all  to  show  that  the  moon  actually 
does  fall  towards  the  earth  just  as  rapidly  as  a  stone  would 
if  it  were  in  the  same  circumstances.  Using  the  best 
information  then  attainable  as  to  the  distance  of  the 
moon,  Newton  calculated  that  the  moon  falls  through  the 
space  of  13  feet  in  one  minute,  but  that  a  stone,  if  elevated 
so  high,  would  fall  through  15  feet  Most  men  would 
have  considered  this  approach  to  coincidence  as  a  proof 
of  his  theory,  but  Newton's  love  of  certain  truth  rendered 
him  different  even  from  most  philosophers,  and  the  dis- 
crepancy caused  him  to  lay  "  aside  at  that  time  any  fur- 
ther thoughts  of  this  matter." 

It  was  not  till  many  years  afterwards  (probably  15 
or  1 6)  that  Newton,  hearing  of  some  more  exact  data 
from  wkkh  he  could  calculate  the  distance  of  the  moon, 


962         EMPIRICAL  AND  DEDUCTIVE      [LESS 

was  able  to  explain  the  discrepancy.  His  theory  of  gra- 
vitation was  then  verified  so  far  as  the  moon  was  con- 
cerned ;  but  this  was  to  him  only  the  beginning  of  a  long 
course  of  deductive  calculations,  each  ending  in  a  verifica- 
tion. If  the  earth  and  moon  attract  each  other,  and  also 
the  sun  and  the  earth,  similarly  there  is  no  reason  why 
the  sun  and  moon  should  not  attract  each  other.  Newton 
followed  out  the  consequences  of  this  inference,  and  showed 
that  the  moon  would  not  move  as  if  attracted  by  the 
earth  only,  but  sometimes  faster  and  sometimes  slower. 
Comparisons  with  Flamsteed's  observations  of  the  moon 
showed  that  such  was  the  case.  Newton  argued  again, 
that  as  the  waters  of  the  ocean  are  not  rigidly  attached  to 
the  earth,  they  might  attract  the  moon,  and  be  attracted 
in  return,  independently  of  the  rest  of  the  earth.  Certain 
daily  motions  would  then  be  caused  thereby  exactly 
resembling  the  tides,  and  there  were  the  tides  to  verify 
the  fact  It  was  the  almost  superhuman  power  with 
which  he  traced  out  geometrically  the  consequences  of  his 
theory,  and  submitted  them  to  repeated  comparison  with 
experience,  which  constitutes  his  preeminence  over  all 
philosophers. 

What  he  began  has  been  going  on  ever  since.  The 
places  of  the  moon  and  planets  are  calculated  for  each 
day  on  the  assumption  of  the  absolute  truth  of  Newton's 
law  of  gravitation.  Every  night  their  places  are  observed 
as  far  as  possible  at  Greenwich  or  some  other  observatory; 
comparison  of  the  observed  with  the  predicted  place  is 
always  in  some  degree  erroneous,  and  if  coincident  would 
be  so  only  by  accident.  The  theory  is  never  proved  com- 
pletely true,  and  never  can  be ;  but  the  more  accurately  the 
results  ef  the  theory  are  calculated,  and  the  more  perfect 
the  instruments  of  the  astronomer  are  rendered,  the  more 
close  is  the  correspondence.  Thus  the  rude  observations 
«f  Kepler  and  the  few  slight  facts  which  worked  on  New 


XXX.J  METHODS.  j6» 

ton's  mind,  were  the  foundation  of  a  theory  which  yielded 
indefinite  means  of  anticipating  new  facts,  and  by  con- 
stant verification,  as  far  as  human  accuracy  can  go,  has 
been  placed  beyond  all  reasonable  doubt. 

Were  space  available  it  might  be  shown  that  all  otha 
great  theories  have  followed  nearly  the  same  course. 
The  undulatory  theory  of  sound  was  in  fact  almost  verified 
by  Newton  himself,  though  when  he  calculated  from  it 
the  velocity  of  sound  there  was  again  a  discrepancy,  which 
only  subsequent  investigation  could  explain.  This  theory 
no  doubt  suggested  the  corresponding  theory  of  light, 
which  when  followed  out  by  Young,  Fresnel,  and  others, 
always  gave  results  which  were  ultimately  in  harmony 
with  observation.  It  even  enabled  mathematicians  to 
anticipate  results  which  the  most  ardent  imagination 
could  hardly  have  guessed,  and  which  mere  haphazard 
experiment  might  never  have  revealed.  Dalton's  laws  ol 
equivalent  proportions  in  chemistry,  if  not  his  atomic 
theory,  were  founded  on  experiments  made  with  the 
simplest  and  rudest  apparatus,  but  results  deduced  from 
them  are  daily  verified  in  the  nicest  processes  of  modern 
chemical  analysis.  The  still  more  modern  theory  of  the 
Conservation  of  Energy,  which  had  been  vaguely  antici- 
pated by  Bacon,  Rumford,  Montgolfier,  Seguin,  Mayer 
and  possibly  others,  was  by  Mr  Joule  brought  to  the  test 
of  experimental  verification  in  some  of  the  most  beautiful 
and  decisive  experiments  which  are  on  record.  It  will  be 
long  before  scientific  men  shall  have  traced  out  all  the 
consequences  of  this  grand  principle,  but  its  correspond' 
ence  with  fact  already  places  it  far  beyond  doubt 

It  will  now  be  apparent,  I  think,  that  though  observa- 
tion and  induction  must  ever  be  the  ground  of  all  certain 
knowledge  01  nature,  their  unaided  employment  could 
never  have  led  to  the  results  of  modern  science.  He  who 
merely  collects  and  digests  facts  will  seldom  acquire  a 


204  EXPLANATION,   TENDENCY,       [LESS 

comprehension  of  their  laws.  He  who  frames  a  theor> 
and  is  content  with  his  own  deductions  from  it,  like  Des- 
cartes, will  only  surprise  the  world  with  his  misused 
genius  ;  but  the  best  student  of  science  is  he  who  with  a 
copious  store  of  theories  and  fancies  has  the  highest 
power  of  foreseeing  their  consequences,  the  greatest  dili- 
^en.e.  in  comparing  them  with  undoubted  facts,  and  the 
greatest  candour  in  confessing  the  ninety-nine  mistakes 
he  has  made  in  reaching  the  one  true  law  of  nature. 


LESSON  XXXI. 

EXPLANATION,     TENDENCY,    HYPOTHESIS, 
THEORY,  AND   FACT. 

IN  the  preceding  Lessons  I  have  used  several  expressions 
of  which  the  meaning  has  not  been  defined.  It  will  now 
be  convenient  to  exemplify  the  use  of  these  terms,  and  tc 
arrive  as  far  as  possible  at  a  clear  understanding  of  their 
proper  meanings. 

Explanation  is  literally  the  making  plain  or  clear,  so 
that  there  shall  be  nothing  uneven  or  obscure  to  inter- 
rupt our  view.  Scientific  explanation  consists  in  harmo- 
nizing fact  with  fact,  or  fact  with  law,  or  law  with  law, 
so  that  we  may  see  them  both  to  be  cases  of  one  uniform 
law  of  causation.  If  we  hear  of  a  great  earthquake  in 
>ome  part  of  the  world  and  subsequently  hear  that  a 
eighbouring  volcano  has  broken  out,  we  say  that  the 
.arthquake  is  thus  partially  explained.  The  eruption 
ihows  that  there  were  great  forces  operating  beneath  the 
;arth's  surface,  and  the  earthquake  is  obviously  an  effect 
Df  such  causes.  The  scratches  which  may  be  plainly  seen 
upon  the  surface  of  rocks  in  certain  parts  of  Wales  and 
Cumberland,  are  explained  by  the  former  existence  of  gla- 
tiers  in  those  mountains ;  the  scratches  exactly  hanroniif 


xxxi.]  HYPOTHESIS,  THEORY,  AND  FACT.  265 

with  the  effects  of  glaciers  now  existing  in  Switzerland, 
Greenland,  and  elsewhere.  These  may  be  considered  «- 
planattons  of  fact  by  fact. 

A  fact  may  also  be  explained  by  a  general  law  ol 
nature,  that  is  the  cause  and  mode  of  its  'production  may 
be  pointed  out  and  shown  to  be  the  same  as  operates  in 
many  apparently  different  cases.  Thus  the  cracking  ol 
glass  by  heat  was-  explained  (p.  257)  as  one  result  of  the 
universal  law  that  heat  increases  the  dimensions  of  solid 
bodies.  The  trade-winds  are  explained  as  one  case  of 
the  general  tendency  of  warm  air  to  rise  and  be  displaced 
by  cold  and  dense  air.  The  very  same  simple  laws  of  heat 
and  mechanics  which  cause  a  draught  to  flow  up  a  chimney 
when  there  is  a  fire  below,  cause  winds  to  blow  from  each 
hemisphere  towards  the  equator.  At  the  same  time  the 
easterly  direction  from  which  the  winds  come  is  explained 
by  the  simplest  laws  of  motion ;  for  as  the  earth  rotates 
from  west  to  east,  and  mores  much  more  rapidly  at  the 
equator  than  nearer  the  poles,  the  air  tends  to  preserve 
its  slower  rate  of  motion,  and  the  earth  near  the  equator 
moving  under  it  occasions  an  apparent  motion  of  the  wind 
from  east  to  west. 

There  are,  according  to  Mr  Mill,  three  distinct  ways 
in  which  one  law  may  be  explained  by  other  laws,  or 
brought  into  harmony  with  them. 

The  first  is  the  case  where  there  are  really  two 
or  more  separate  causes  in  action,  the  results  of  which 
are  combined  or  added  together,  homogeneously.  As 
was  before  explained,  homogeneous  Intermixture  of  effects 
(p.  252)  means  that  the  joint  effect  is  simply  the  sum  of  tht 
separate  effects,  and  is  of  the  same  kind  with  them.  GUI 
last  example  of  the  trade-winds  really  comes  under  thii 
case,  for  we  find  that  there  is  one  law  or  tendency  which 
causes  winds  to  blow  from  the  arctic  regions  toward*  tht 
equator,  and  a  second  tendency  which  causes  then  to  blo« 


266  EXPLANATION,  TENDENCY,        [LESS 

from  east  to  west  These  tendencies  are  combined  to 
gether,  and  cause  the  trade- winds  to  blow  from  the  North- 
Ernst  in  the  northern  hemisphere,  and  from  the  South- East 
in  the  southern  hemisphere.  The  law  according  to  which 
ihe  temperature  of  the  air  is  governed  in  any  part  of  the 
earth  is  a  very  complicated  one,  depending  partly  on  the 
law  by  which  the  sun's  heating  power  is  governed,  partly 
on  the  power  of  the  earth  to  radiate  the  heat  away  into 
space,  but  even  more  perhaps  on  the  effect  of  currents  of 
air  or  waier  in  bringing  warmth  or  carrying  k  away. 
The  path  of  a  cannon-ball  or  other  projectile  is  deter- 
mined by  the  joint  action  of  several  laws ;  firstly,  the 
simple  law  of  motion,  by  which  any  moving  body  tends 
to  move  onward  at  an  uniform  rate  in  a  straight  line ; 
secondly,  the  law  of  gravity,  which  continually  deflects 
the  body  towards  the  earth's  surface ;  thirdly,  the  resist- 
ance of  the  air,  which  tends  to  diminish  its  velocity. 

The  reader  will  perhaps  have  noticed  the  frequent  use 
of  the  word  tendency,  and  I  have  repeatedly  spoken  of  a 
cause  as  tending  to  produce  its  effect  If  the  joint  and 
homogeneous  action  of  causes  has  been  clearly  explained, 
it  will  now  be  clear  that  a  tendency  means  a  cause  which 
will  produce  an  effect  unless  there  be  opposite  causes, 
which,  in  combination  with  it,  counteract  and  disguise 
that  effect  Thus  when  we  throw  a  stone  into  the  air  the 
attractive  power  of  the  earth  tends  to  make  it  fall,  out  the 
upward  motion  we  have  impressed  upon  it  disguises  th< 
result  for  a  certain  time.  The  interminable  revolving 
motion  of  the  moon  round  the  earth  is  the  result  of  two 
balanced  tendencies,  that  towards  the  earth,  and  that  tc 
proceed  onward  in  a  straight  line.  The  laws  of  motior. 
and  gravity  are  such  that  this  balance  must  always  be 
preserved ;  if  the  moon  by  any  cause  were  brought  nearei 
to  the  earth  its  tendency  to  fly  off  would  be  increased, 
and  would  exceed  the  effect  of  gravity  until  it  had  regained 


XXXI.  J  HYPOTHESIS,  THEORY,  AND  FACT. 


its  proper  distance.     A  tendency  then  is  a  cause 
may  or  may  not  be  counteracted. 

In  the  second  case  of  explanation  an  effect  is  shown 
to  be  due,  not  to  the  supposed  cause  directly,  but  to  an 
Intermediate  effect  of  t&at  cause.  Instead  of  A  being  thf 
ca-ise  of  C,  it  is  found  that  A  is  the  cause  of  /?,  and  b  the 
:ause  of  C,  so  that  B  constitutes  an  Intermediate  link, 
This  explanation  may  seem  to  increase  the  complexity  of 
the  matter,  but  it  really  simplifies  it  ;  for  the  connection  of 
A  with  B  may  be  a  case  of  a  familiar  and  simple  law,  and 
so  may  that  of  B  with  C  ;  whereas  the  law  that  A  pro- 
duces C  may  be  purely  empirical  and  apparently  out  of 
harmony  with  everything  else.  Thus  in  lightning  it 
seems  as  if  electricity  had  the  power  of  creating  a  loud 
explosion  ;  but  in  reality  electricity  only  produces  heat, 
and  it  is  the  heat  which  occasions  sound  by  suddenly 
expanding  the  air.  Thus  thunder  comes  into  harmony 
with  the  sound  of  artillery,  which  is  also  occasioned  by 
the  sudden  expansion  of  the  heated  gases  emitted  by  the 
powder.  When  chlorine  was  discovered  it  was  soon  found 
to  have  a  strong  power  of  bleaching,  and  at  the  present 
day  almost  all  bleaching  is  done  by  chlorine  instead  of 
the  sun,  as  formerly.  Inquiry  showed  however  that  k  was 
not  really  the  chlorine  which  destroyed  colour,  but  that 
oxygen  is  the  intermediate  and  active  agent  Chlorine 
decomposes  water,  and  taking  the  hydrogen  leaves  the 
oxygen  in  a  state  of  great  activity  and  ready  to  destroy 
the  organic  colouring  matter.  Thus  a  number  of  facts 
are  harmonized  ;  we  learn  why  dry  chlorine  does  not 
bleach,  and  why  there  are  several  other  substances  which 
resemble  chlorine  in  its  bleaching  power,  for  instance, 
ozone,  peroxide  of  hydrogen,  sulphurous  acid,  and  a  pecu- 
liar oxide  of  vanadium,  lately  discovered  by  Dr  Roscoe. 
It  would  be  impossible  to  understand  the  effect  at  all  un- 
less we  knew  that  it  is  probably  due  to  active  oxygen  01 


068  EXPLANATION,  TENDENCY,        [ucsa 

ozone  in  all  the  cases,  even  in  the  old  method  of  bleach- 
ing by  exposure  to  the  sun  *. 

The  third  and  much  more  important  case  of  e» 
planation  is  where  one  law  is  shown  to  be  a  ease  of  • 
more  general  law.  As  was  explained  in  Lesson  xxiv.  we 
naturally  discover  the  less  general  first,  and  gradually 
penetrate  to  the  more  simple  but  profound  secrets  o< 
naturt.  It  has  often  been  found  that  scientific  men  were 
in  possession  of  several  well-known  laws  without  perceiv- 
ing the  bond  which  connected  them  together.  Men,  for 
instance,  had  long  known  that  all  heavy  bodies  tended  to 
fall  towards  the  earth,  and  before  the  time  of  Newton  it 
was  known  to  Hooke,  Huyghens,  and  others,  that  some 
force  probably  connected  the  earth  with  the  sun  and  moon. 
It  was  Newton,  however,  who  clearly  brought  these  and 
many  other  facts  under  one  general  law,  so  that  each  fact 
or  less  general  law  throws  light  upon  every  other. 

The  science  of  Electricity  now  harmonizes  a  vast 
series  of  partial  laws  and  facts  between  which  it  was 
a  truly  difficult  task  to  discover  any  resemblance.  The 
chief  properties  of  the  magnet  had  been  fairly  known 
since  the  time  of  Gilbert,  the  physician  of  Queen  Elixa- 
beth  ;  common  frictional  electricity  was  carefully  stu- 
died by  Otto  von  Guericke,  Epinus,  Coulomb,  and  others  ; 
Galvanism  was  elaborately  investigated  almost  as  soon 
as  Galvani  and  Volta  discovered  the  fact  that  the  che- 
mical action  of  one  substance  on  another  may  produce 
electricity.  In  the  early  part  of  this  century  there  were 
three  distinct  sciences,  Magnetism,  Electricity  and  Gal- 
vanism ;  now  there  is  but  one  science.  Oersted  at 
Copenhagen  gave  in  1819  the  first  link  between  them,  by 
pointing  out  that  an  electric  current  may  cause  move- 
taeats  in  a  compass-needle.  Ampere  and  Faraday  worked 

•  Watts'  Diftitnoy  of  Chtmistry,  VoL  I.  p.  foi. 


xxxi.]  HYPOTHESIS,  THEORY,  AND  FACT  269 

out  the  complicated  relations  of  the  three  sciences,  com- 
prehending them  finally  in  a  wider  science,  which  may  be 
called  Electro-magnetism,  or  we  may  perhaps  conveniently 
generalize  the  name  Electricity  so  as  to  comprehend  all 
the  phenomena  connected  with  it 

A  number  of  minor  laws  and  detached  facts  are  com- 
prehended and  explained  in  the  theory  now  generally 
accepted,  that  heat,  electricity,  light,  and  in  fact  all  the 
phenomena  of  nature,  are  but  manifestations  in  different 
forms  of  one  same  kind  of  energy.  The  total  amount  of 
energy  existing  in  the  universe  is  held  to  be  fixed  and  un- 
alterable, like  the  quantity  of  matter  ;  sometimes  it  is 
disguised  by  affecting  only  the  insensible  molecules;  at 
other  times  it  is  seen  to  produce  palpable  mechanical 
effects,  as  in  the  fall  of  a  stone,  or  the  expansion  of 
steam.  Now  it  had  been  previously  known,  ever  since  the 
time  of  the  Greeks,  that  a  simple  lever,  although  greatly 
altering  the  character  of  force  by  making  its  action  slower 
or  faster,  does  not  alter  its  amount,  because  the  more 
intense  the  force  the  slower  and  more  limited  is  its  action. 
In  modern  times  a  similar  truth  was  proved  of  every  kind 
of  machine ;  and  it  was  recognised  that,  apart  from  friction, 
no  kind  of  mechanism  either  creates  or  destroys  energy. 
It  had  been  independently  recognised  that  electricity 
produced  in  the  galvanic  battery  was  exactly  proportional 
to  the  amount  of  chemical  action,  and  that  almost  any 
one  of  the  forces  named  could  be  converted  into  any  one 
of  the  others.  All  such  facts  are  now  comprehended 
under  one  general  theory,  the  details  of  which  are  being 
gradually  rendered  more  certain  and  accurate,  but  th< 
main  principle  of  which  is  that  a  certain  amount  of  me- 
chanical energy  is  equal  to  a  certain  amount  of  heat,  a 
certain  amount  of  electricity,  of  chemical  action,  or  even 
of  muscular  exertion. 

The  word  hypothesis  is  much  used  ia  connection  will 


iTO  EXPLANATION,  TENDENCY,        [l 

the  subject  we  are  discussing,  and  its  meaning  must  be 
considered.  It  is  derived  from  the  Greek  words  wr«, 
under,  and  6kw,  placing,  and  is  therefore  exactly  synony- 
mous with  the  Latin  word  supposttio,  a  placing  under 
whence  our  common  word  supposition.  It  appears  tc 
mean  in  science  the  imagining  of  some  thing,  force  01 
cause,  which  underlies  the  phenomena  we  are  examining 
and  is  the  agent  in  their  production  without  being  capable 
of  direct  observation.  In  making  a  hypothesis  we  assert 
the  existence  of  a  cause  on  the  ground  of  the  effects 
observed,  and  the  probability  of  its  existence  depends 
upon  the  number  of  diverse  facts  or  partial  laws  that  we 
are  thus  enabled  to  explain  or  reduce  to  harmony.  To  be 
of  any  value  at  all  a  hypothesis  must  harmonize  at  least 
two  different  facts.  If  we  account  for  the  effects  of  opium 
by  saying  with  Moliere  that  it  possesses  a  dormitive 
power,  or  say  that  the  magnet  attracts  because  it  has  a 
magnetic  power,  every  one  can  see  that  we  gain  nothing. 
We  know  neither  more  nor  less  about  the  dormitive  or 
magnetic  power  than  we  do  about  opium  or  the  magnet. 
But  if  we  suppose  the  magnet  to  attract  because  it  is 
occupied  by  circulating  currents  of  electricity  the  hypo- 
thesis may  seem  a  very  improbable  one,  but  is  valid, 
because  we  thus  draw  a  certain  analogy  between  a  magnet 
and  a  coil  of  wire  conveying  electricity.  Such  a  coil  of 
wire  attracts  other  coils  exactly  in  the  way  that  one  mag- 
net attracts  another  ;  so  that  this  hypothesis  enables  us 
to  harmonize  several  different  facts.  The  existence  of 
intense  heat  in  the  interior  of  the  earth  is  hypothetical  in 
so  far  as  regards  the  impossibility  of  actually  seeing  and 
measuring  the  heat  directly,  but  it  harmonizes  so  many 
facts  derived  from  different  sources  that  we  can  hardly 
doubt  its  existence.  Thus  the  occurrence  of  hot  springs 
and  volcanoes  are  some  facts  in  its  favour,  though  they 
might  be  explained  on  other  grounds ;  the  empirical  lav 


<xxi.]  HYPOTHESIS,  THEORY,  AND  FACT.  271 

that  the  heat  increases  as  we  sink  mines  in  any  part  ol 
the  earth's  surface  is  stronger  evidence.  The  mtenselv 
heated  condition  of  the  sun  and  other  stars  is  strongly 
confirmatory  as  showing  that  other  bodies  do  exist  in  the 
supposed  condition  of  the  earth's  interior.  The  cool 
state  of  the  earth's  surface  is  perfectly  consistent  with  its 
comparatively  small  size  and  the  known  facts  and  laws 
concerning  the  conduction  and  radiation  of  heat  And 
the  more  we  learn  concerning  the  way  in  which  the  sun's 
heat  is  supplied  by  the  fall  of  meteoric  matter,  the  more 
it  is  probable  that  the  earth  may  have  been  intensely 
heated  like  the  sun  at  some  former  time,  although  for  an 
immense  period  it  has  been  growing  slowly  colder.  A 
supposition  coinciding  with  so  many  facts,  laws,  and  other 
probable  hypotheses,  almost  ceases  to  be  hypothetical! 
and  its  high  probability  causes  it  to  be  regarded  as  a 
known  fact. 

Provided  it  is  consistent  with  the  laws  of  thought  there 
is  nothing  that  we  may  not  have  to  accept  as  a  probable 
hypothesis,  however  difficult  it  may  be  to  conceive  and 
understand.  The  force  of  gravity  is  hypothetical  in  so 
far  that  we  know  it  only  by  its  effects  upon  the  motions 
of  bodies.  Its  decrease  at  a  distance  harmonizes  exactly 
indeed  with  the  way  in  which  light,  sor.nd,  electric  or 
magnetic  attractions,  and  in  fact  all  influences  which 
emanate  from  a  point  and  spread  through  space,  decrease  ; 
hence  it  is  probable  that  the  law  of  the  inverse  square  is 
absolutely  true.  But  in  other  respects  gravity  is  strongly 
opposed  to  all  our  ideas.  If  sound  could  travel  to  the 
sun  as  rapidly  as  in  the  earth's  atmosphere  it  would  re- 
quire nearly  fourteen  years  to  reach  its  destination  ;  were 
the  sun  and  earth  united  by  a  solid  continuous  bar  of  iron, 
»  strong  pull  at  one  end  would  not  be  felt  at  the  othei 
until  nearly  three  years  had  passed.  Light  indeed  comes 
from  the  sun  in  rather  more  than  eight  minutes ;  but  what 


2?2  EXPLANA  T1ON,  TENDENCY, 

are  we  to  think  of  the  force  of  gravity,  which  appears  U 
reach  the  sun  in  an  instant — so  short  that  no  calculation! 
have  yet  been  able  to  detect  any  interval  at  all?  In  fact 
there  seems  some  reason  to  suppose  that  gravity  is  felt 
instantaneously  throughout  the  immeasurable  regions  ol 
space. 

The  undulatory  hypothesis  of  light  presents  feature* 
equally  extraordinary  and  inconceivable.  That  light  does 
consist  of  minute  but  excessively  rapid  vibrations  of 
something  occupying  space,  is  almost  certain,  because  of 
the  great  harmony  which  this  hypothesis  introduces  into 
the  exceedingly  various  and  complicated  phenomena  of 
light,  and  the  explanation  which  it  affords  of  the  analog)' 
of  light  to  sound  It  is  difficult  indeed  to  imagine  that 
anything  can  oscillate  so  rapidly  as  to  strike  the  retina 
of  the  eye  831479,000,000,000  in  one  second,  as  must  be 
the  case  with  violet  light  according  to  this  hypothesis. 
But  this  is  nothing  to  the  difficulty  of  imagining  space  to 
be  filled  with  solid  ether  of  extreme  rigidity  and  elasticity, 
but  which  nevertheless  offers  no  appreciable  resistance  to 
the  passage  through  it  of  ordinary  matter,  and  does  not 
itself  possess  any  gravity*.  It  has  been  asserted  indeed 
that  the  retardation  in  the  return  of  comets  is  due  to 
friction  against  this  ether,  and  Mr  Balfour  Stewart  be- 
lieves he  has  produced  heat  by  friction  of  a  metallic  disc 
against  the  ether  in  a  vacuum.  Should  these  assertions 
prove  to  be  true  we  have  new  facts  ir  harmony  with  the 
theory  of  light,  which  would  thereby  become  less  hypo- 
thetical than  before. 

There  is  no  difficulty  now  in  perceiving  the  part  which 
hypothesis  plays  in  the  deductive  method  of  scientific 
investigation  considered  in  the  lost  lesson.  The  pre- 
liminary induction  is  replaced  more  or  less  completely  by 

*  See  Sir  John  Herschel's  Familiar  Ltetwres,  p.  315,  Jko 


xxxi.]  HYPOTHESIS,  THEORY,  AND  FACT.  373 

imagining  the  existence  of  agents  which  we  think  adequate 
to  produce  the  known  effects  in  question.  If  it  is  oui 
object  to  explain  the  causes  of  ebbing  and  flowing  wells, 
which  occur  in  many  parts  of  the  world,  we  cannot 
possibly  proceed  by  first  exploring  the  interior  of  the 
•arth,  until  we  can  discover  the  source  of  a  spring,  and 
observe  its  circumstances.  We  are  obliged  to  imagine 
cavities  and  channels  of  various  forms,  until  we  conceive 
such  an  apparatus  as  will,  in  accordance  with  known  laws 
of  hydrostatics,  occasion  the  irregular  flowing  of  water  in 
the  way  observed.  If  we  can  show  that  cavities  of  a 
particular  form  will  produce  that  effect,  and  can  think  of 
no  other  mode  in  which  it  could  be  produced,  the  hypo- 
thesis becomes  established  as  almost  a  certain  fact 

It  is  the  same  with  any  great  hypothesis  like  that  of  the 
theory  of  light  We  have  no  means  of  directly  observing 
and  measuring  the  qualities  of  the  ether  which  is  the 
medium  of  light  All  we  know  about  this  ether  at  present 
is  derived  from  the  observed  phenomena  of  light.  Hence 
we  are  driven  to  invent  something  and  endow  it  with 
qualities  from  which  we  may  calculate,  according  to  some 
of  the  principles  of  mechanics,  the  effect  to  be  expected  ; 
and  finding  that  these  effects  may  be  made  to  harmonize 
with  those  actually  observed,  we  depend  upon  this  coinci- 
dence to  prove  the  existence  of  the  ether.  The  truth  of 
a  hypothesis  thus  altogether  depends  upon  subsequent 
verification  and  accordance  with  observed  facts.  To 
invent  hypotheses  which  cannot  thus  be  verified,  or  to 
invent  them  and  then  neglect  the  verification,  leads  to  no 
result  at  all,  or  to  fallacy.  But  when  the  verification  is 
careful  and  complete  no  reproach  can  be  brought  against 
the  employment  of  hypothesis.  It  becomes,  perhaps,  as 
certain  as  any  other  mode  of  investigation,  and  is  at  any 
rate  indispensable.  There  was,  in  fact,  little  truth  at 
reason  in  Newton's  celebrated  protest  against  the  use  of 

18 


274  EXPLANATION,  TENDENCY,       [LFS& 

hypothesis — "  Hypotheses  non  fingo."  The  fact  is  that  ai 
his  theory  of  gravitation  rested  upon  the  greatest  and 
most  successful  of  hypotheses,  so  his  views  of  the  material 
nature  of  light  and  the  causes  of  its  peculiar  phenomena 
involved  a  false  hypothesis,  which  has  long  since  been 
completely  disproved. 

The  word  theory  has  constantly  been  used  in  the 
last  few  lessons,  and  deserves  some  examination.  It 
comes  from  the  Greek  tffwpto,  meaning  contemplation, 
reflection  or  speculation;  but  this  gives  us  little  clue  to  its 
modern  use.  In  reality  the  word  is  highly  ambiguous, 
being  sometimes  used  as  equivalent  to  hypothesis,  at 
other  times  as  equivalent  to  general  law  or  truth.  When 
peopte  form  theories  concerning  comets,  the  sun,  the 
cause  of  earthquakes,  &c.,  they  imagine  a  great  many 
things  which  may  or  may  not  exist ;  such  theories  are 
really  complicated  hypotheses,  and  should  be  so  called. 
In  this  sense  there  are  two  theories  of  electricity,  one  of 
which  supposes  the  existence  of  a  single  fluid  which 
accumulates  in  some  places  and  has  then  a  tendency  to 
discharge  itself  towards  places  where  there  is  a  deficiency, 
just  as  water  always  tends  to  find  its  level;  the  other 
supposes  the  existence  of  two  fluids  which  are  commonly 
united,  but  when  separated  tend  to  rush  back  into  union 
again.  These  so-called  theories  are  really  hypotheses,  be- 
cause we  have  no  independent  evidence  of  the  existence 
of  any  fluid,  and  it  is  now  almost  certain  that  there  is  no 
such  thing.  The  atomic  theory,  again,  is  really  a  hypo- 
thesis suggested  by  Dalton  to  explain  the  remarkable 
laws  which  he  detected  in  the  proportions  of  chemical 
elements  which  combine  together.  It  is  a  valid  hypothesis 
in  so  far  as  it  does  really  explain  the  fixedness  of  the 
quantities  which  combine;  but  it  is  purely  hypothetical 
u  regards  the  shapes,  properties  or  absolute  magnitude* 
of  the  atoms,  because  we  have  no  facts  which  it  can  hai 


xxxi]  HYPOTHESIS,  THEORY,  AND  FACT.  275 

monise  in  these  respects,   and  no  apparent  means  of 

gaining  them. 

In  another  and  more  proper  sense  theory  is  opposed 
to  practice,  just  as  the  general  is  opposed  to  the  particular 
The  theory  of  gravitation  means  all  the  more  general  laws 
of  motion  and  attraction  on  which  Newton  founded  his 
system  of  the  Universe.  We  may  know  what  those  laws 
are  without  being  able  to  determine  the  place  of  a  planet 
or  make  any  practical  use  of  them ;  the  particular  results 
must  be  calculated  out  by  skilful  astronomers  before 
navigators,  travellers  or  others  can  make  practical  use  of 
them  in  the  determination  of  the  latitude  or  longitude. 
When  we  speak  of  the  mathematical  theory  of  sound,  the 
omar  theory,  the  theory  of  the  tides,  the  word  is  employed 
without  any  special  reference  to  hypothesis,  and  is  merely 
equivalent  to  general  knowledge  or  science,  implying  the 
possession  of  a  complete  series  of  general  and  accurate 
laws,  but  in  no  way  distinguishing  them  from  accurate 
knowledge  in  general  When  a  word  is  really  used  in  an 
equivocal  manner  like  theory,  it  is  not  desirable  to  attempt 
to  give  it  an  accurate  definition  which  would  be  imagi- 
nary and  artificial 

The  word  fact  is  used  very  often  in  this  as  in  most 
books,  and  demands  a  few  remarks.  It  is  derived  from 
factum,  the  past  participle  of  facere,  to  do,  and  would 
thus  mean  something  which  is  done,  an  act,  or  deed ;  but 
the  meaning  is  evidently  greatly  extended  by  analogy. 
We  usually  oppose  to  each  other  fact  and  theory,  but  just 
as  theory  seems  to  have  two  ambiguous  meanings,  so 
I  believe  that  fact  is  ambiguous.  Sometimes  it  means 
what  is  certain  and  known  by  the  evidence  of  the  senses, 
is  opposed  to  what  is  known  only  probably  by  hypothesis 
and  inference ;  at  other  times  it  is  contrasted  to  a  general 
law,  and  is  equivalent  to  a  particular  instance  or  case.  A 
law  of  great  generality  may  often  be  as  certain  and  true, 

1 8— a 


*70  CLASS 'IFICA  TfON,  fLE» 

especially  in  mathematics,  as  the  particular  facts  coming 
under  it,  so  that  the  contrast  must  in  this  case  be  that 
between  the  general  and  particular.  We  often  use  the 
word  too  in  common  life,  as  merely  equivalent  to  truth j 
:hus  we  might  say,  "It  is  a  fact  that  the  primary  laws  of 
thought  are  the  foundation  of  reasoning."  In  short,  as 
.heory  means  ambiguously  what  is  hypothetical,  general, 
abstract  or  uncertain,  so  fact  is  equally  ambiguous,  and 
means  confusedly  what  is  intuitively  known,  particular, 
concrete  or  certain. 

Mill's  System  of  Logic,  Book  in.  Chapters  12,  13  and 
14,  Of  Explanation,  and  Hypothesis. 


LESSON   XXXII. 
CLASSIFICATION,   AND  ABSTRACTION. 

IN  an  earlier  Lesson,  upon  the  subject  of  the  Predicables, 
we  considered  the  doctrine  of  classification  as  it  was 
treated  by  logicians  many  centuries  ago.  The  progress 
of  science,  however,  during  the  last  two  centuries  has 
caused  great  attention  to  be  given  to  the  true  principles 
on  which  we  can  arrange  a  great  multitude  of  diverse 
objects  in  order,  and  we  have  to  consider  what  are  the 
characteristics  of  a  natural  and  perfect  system  of  classifi- 
cation. 

It  maybe  said,  indeed,  that  the  subject  we  are  treating 
b  coextensive  with  the  science  of  logic.  All  thought,  al] 
reasoning,  so  far  as  it  deals  with  general  names  or  general 
ootions,  may  be  said  to  consist  in  classification.  Ever* 
common  or  general  name  is  the  name  of  a  class,  and  every 
name  of  a  class  is  a  common  name.  "  Metal"  is  the  name 


xxxn.]  AND  ABSTRACTION.  177 

of  one  class  of  substances  so  often  used  in  our  syllogistic 

sfcamples ;  "  Element"  of  another  class,  of  which  the  formei 
class  is  part.  Reasoning  has  been  plausibly  represented 
to  consist  in  affirming  of  the  parts  of  a  class  whatever 
may  be  affirmed  of  the  whole.  Every  law  of  nature  which 
we  arrive  at  enables  us  to  classify  together  a  numbei  oi 
facts,  and  it  would  hardly  be  too  much  to  define  logic  ai 
the  theory  of  classification. 

Here  we  deal,  however,  with  that  more  conscious  and 
distinct  arrangement  of  objects  or  notions,  which  is  espe- 
cially employed  in  the  natural  sciences,  such  as  Botany, 
Zoology,  Mineralogy  and  Palaeontology. 

The  derivation  of  the  word  class  is  semewhat  curious. 
In  ancient  Rome  it  was  the  practice  to  summon  the 
whole  people  together  at  certain  periods,  and  this  cere- 
mony was  known  as  a  clasis,  from  the  Greek  *Ad<rtf,  or 
vXqcrtr,  derived  from  coXcc*,  to  call  together.  Servius 
Tullius  is  said  to  have  divided  the  people  into  six  orders, 
according  to  the  amount  of  tribute  they  could  pay,  and 
these  orders  were  not  unnaturally  called  the  classes  of  the 
people.  Hence  the  name  came  by  degrees  to-be  applied 
to  any  organized  body  of  people,  such  as  an  army ;  thence 
it  was  transferred  to- a  fleet  of  vessels  as  marshalled  in  a 
fixed  order,  and  was  finally  extended  by  analogy  to  any 
collection  of  objects  carefully  arranged.  When,  however, 
we  now  speak  of  the  lower  or-higher  classes  of  the  people 
it  is  curious  that  we  are  restoring  the  word  very  nearlyto 
f,ts  original'meaning. 

Classification  may  perhaps  be  best  defined  as  the  or- 
rangement  of  things,  or  our  notions  of  them,  according  t* 
their  resemblances  or  identities.  Every  class  should  so 
be  constituted  as  to  contain  objects  exactly  resembling 
each  other  in  certain  definite  qualities,  which  are  stated 
in  the  definition  of  the  class.  The  more  numerous  and 
e*tensive  the  resemblances  which  are  thus  indicated  bf 


•78  CLASSIFICATION^ 

any  system  of  classes,  toe  more  perfect  and  useful  most 
that  system  be  considered. 

Mr  Mill  thus  describes  his  view  of  the  meaning— 
"Classification  is  a  contrivance  for  the  best  possible 
ordering  of  the  ideas  of  objects  in  our  minds  ;  for  causing 
the  ideas  to  accompany  or  succeed  one  another  in  such  a 
way  as  shall  give  us  the  greatest  command  over  our  know- 
ledge  already  acquired,  and  lead  most  directly  to  the 
acquisition  of  more.  The  general  probtem  of  classifica- 
tion, in  reference  to  these  purposei  may  be  stated  as 
follows :  To  provide  that  things  shall  be  thought  of  in 
such  groups,  and  those  groups  in  such  an  order,  as  will 
best  conduce  to  the  remembrance,  and  to  the  ascertain- 
ment of  their  laws." 

A  collection  of  objects  may  generally  be  classified  in  an 
indefinite  number  of  ways.  Any  quality  which  is  possess- 
ed by  some  and  not  by  others  may  be  taken  as  the  first 
difference,  and  the  groups  thus  distinguished  may  be  sub- 
divided in  succession  by  any  other  qualities  taken  at  wilL 
Thus  a  library  of  books  might  be  arranged,  (i)  according 
to  their  size,  (2)  according  to  the  language  in  which  they 
are  written,  (3)  according  to  the  alphabetic  order  of  their 
authors'  names,  (4)  according  to  their  subjects ;  and  in 
various  other  ways.  Iii  large  libraries  and  in  catalogues 
such  modes  of  arrangement  are  adopted  and  variously 
combined.  Each  different  arrangement  presents  some 
peculiar  convenience,  and  that  mode  must  be  selected 
which  best  meets  the  especial  purpose  of  the  library 
or  catalogue.  The  population  of  a  kingdom,  again,  may 
be  classified  in  an  almost  endless  number  of  ways  with 
regard  to  different  purposes  or  sciences.  The  popu- 
lation of  the  United  Kingdom  may  be  divided  according 
to  their  place  of  birth,  as  English,  Welsh,  Scotch,  Irish, 
colonial-born,  and  aliens.  The  ethnographer  would 
divide  them  into  Anglo-Saxons,  Cyrari,  Gaels.  Picti. 


XXXIL]  AND  ABSTRACTION.  37% 

Scandinavians,  &c.  The  statist  arranges  them  accord 
ing  to  age  ;  to  condition,  as  married,  unmarried,  widowed, 
&c. ;  to  state  of  body,  as  able,  incapacitated,  blind,  im- 
becile. The  political  economist  regards  the  innumerable 
trades  which  are  carried  on,  and  classifies  them  in  a 
complex  manner.  The  lawyer  again  treats  every  one  as  a 
minor,  an  adult,  a  feme  sole,  a  feme  couverte,  a  guardian, 
hrard,  trustee,  felon,  and  so  on. 

In  the  natural  world,  again,  we  may  make  various 
classifications.  Plants  may  be  arranged  according  to  the 
country  from  which  they  are  derived ;  the  kind  of  place 
or  habitat  in  which  they  flourish ;  the  time  they  live,  as 
annual,  biennial,  perennial ;  their  size,  as  herbs,  shrubs, 
trees;  their  properties,  as  esculents,  drugs,  or  poisons: 
all  these  are  distinct  from  the  classifications  which  the 
botanist  devises  to  represent  the  natural  affinities  or 
relationships  of  plants.  It  is  thus  evident  that  in  making 
a  classification  we  have  no  one  fixed  method  which  can 
be  ascertained  by  rule,  but  that  an  indefinite  number  of 
choices  or  alternatives  are  usually  open  to  us.  Logic 
cannot  in  such  cases  do  much ;  and  it  is  really  the  work 
of  the  special  sciences  to  investigate  the  character  of  the 
classification  required.  All  that  logic  can  do  is  to  point 
out  certain  general  requirements  and  principles. 

The  first  requisite  of  a  good  classification  is,  that  it 
shall  be  appropriate  to  the  purpose  in  hand  ;  that  is  to 
say,  the  points  of  resemblance  selected  to  form  the  leading 
classes  shall  be  those  of  importance  to  the  practical  use 
of  the  classification.  All  those  things  must  be  arranged 
together  which  require  to  be  treated  alike,  and  those 
things  must  be  separated  which  require  to  be  treated 
separately.  Thus  a  lawyer  has  no  need  to  classify  per- 
sons according  to  the  counties  of  England  they  were  born 
in,  because  the  law  is  the  same  independently  of  counties  ; 
hot  so  far  as  a  Scotchman,  a  Manx  man,  or  an  alien,  tf 


i9o  CLASSIFICATION,  [LESS 

ander  different  laws  from  the  English  born  man,  we  shaft 
require  to  classify  them  apart.  A  gardener  is  quite  right 
In  classifying  plants  as  annuals,  biennials,  perennials;  as 
berbs,  shrubs,  trees;  as  evergreen  and  deciduous;  w 
according  to  the  soil,  temperature  and  other  circumstance* 
which  affect  them,  because  these  are  points  which  must 
puide  him  in  treating  some  differently  from  others. 

Another  and,  in  a  scientific  point  of  view,  the  most 
important  requisite  of  a  good  classification,  is  that  It  shall 
enable  the  greatest  possible  number  of  general  assertions 
to  be  made.  This  is  the  criterion,  as  stated  by  Dr 
Whewell,  which  distinguishes  a  natural  from  an  artificial 
iystem  of  classification,  and  we  must  carefully  dwell  upon 
its  meaning.  It  will  be  apparent  that  a  good  classification 
is  more  than  a  mere  orderly  arrangement ;  it  involves  a 
process  of  induction  which  will  bring  to  light  all  the  more 
general  relations  which  exist  between  the  things  classified 
An  arrangement  of  books  will  generally  be  artificial ;  the 
octavo  volumes  will  not  have  any  common  character  ex- 
cept being  of  an  octavo  size.  An  alphabetical  arrange- 
ment of  names  again  is  exceedingly  appropriate  and  con- 
venient to  many  purposes,  but  is  artificial  because  it 
allows  of  few  or  no  general  assertions.  We  cannot  make 
any  general  assertion  whatever  about  persons  because 
their  names  happen  to  begin  with  an  A  or  a  B,  a  P  or  a 
W.  Even  those  who  agree  in  bearing  the  name  Smith  or 
Taylor  or  Robinson  might  be  submitted  to  the  inductive 
method  of  agreement  without  the  discovery  of  any 
common  circumstance  which  could  be  stated  in  a  general 
proposition  or  law.  It  is  true  that  if  we  investigated  the 
Antecedents  of  the  Evanses  and  Joneses  we  should  find 
them  nearly  all  to  be  Welsh,  and  the  Campbells  to  be 
Scotch,  and  those  who  bear  a  very  peculiar  name  would 
aften  DC  found  to  descend  from  common  ancestors.  So 
tar  even  an  alphabetic  arrangement  embodies  something 


Jtxxn.]  AND  ABSTRACTION.  aSt 

that  is  natural  in  it,  and  enables  general  assertions  to  bi 
made.  Hardly  any  arrangement  can  be  made,  in  fact^ 
which  will  not  indicate  some  vestiges  of  important  rela- 
tions and  resemblances  ;  but  what  we  want  is  a  systerr 
which  will  reveal  all  the  most  important  general  truths. 

For  this  purpose  we  must  select  as  the  ground  ol 
union  those  characters  which  carry  with  them  most  other 
characters.  In  Lesson  xil.  we  considered  the  proprina 
as  a  quality  which  belongs  to  the  whole  of  a  class  without 
forming  part  of  the  definition  of  the  class.  Now  we 
ought  to  frame  the  definition  of  a  class  that  it  may  con 
tain  as  few  characters  as  possible,  but  that  as  many  other 
characters,  properties,  or  propria,  as  possible,  shall  be 
attributable  to  the  things  contained  in  the  class.  Every 
one  can  see,  for  instance,  that  animals  form  one  great 
group  of  beings,  which  have  many  characters  in  common, 
and  that  plants  form  another  group.  Animals  have  sen- 
sation, voluntary  motion,  consume  carbonaceous  food,  and 
evolve  carbonic  acid,  possess  a  stomach,  and  produce 
fat.  Plants  are  devoid  of  sensation  and  voluntary  motion, 
produce  carbonaceous  tissue,  absorb  carbonic  acid,  and 
evolve  oxygen,  possess  no  stomach,  and  produce  starch. 
At  one  time  it  might  have  been  thought  that  almost  any 
of  the  characters  named  was  a  sufficient  mark  of  the 
group  to  which  a  being  belonged.  Whatever  had  a 
stomach,  was  an  animal ;  whatever  had  not,  was  a  plant ; 
whatever  produced  starch  or  evolved  oxygen  was  called  a 
plant  ;  whatever  absorbed  oxygen  or  produced  fat  was  an 
animal  To  the  present  day  these  statements  remain 
generally  true,  so  that  we  may  make  assertions  in  the  form 
of  the  proposition  U,  that  "all  animals  are  all  beings 
that  evolve  carbonic  acid,  and  all  plants  are  all  beings 
that  absorb  carbonic  acid."  But  in  reality  the  exceptions 
are  many,  and  increasing  research  makes  it  continually 
more  apparent  that  there  is  no  definite  line  to  be  draw* 


aft,  CLA  ssi PICA  rion, 

between  animal  and  vegetable  life.  This,  of  course,  is 
not  a  failure  of  logical  science,  but  a  fact  of  great  sig- 
nificance concerning  the  things  themselves. 

ID  a  classification  of  plants  we  meet  again  with  most 
deep  and  natural  distinctions  between  the  great  classes 
called  Exogens,  Endogens,  and  Acrogens.  The  latter 
have  no  true  sexual  flowers  and  seeds,  are  formed  almost 
wholly  of  cellular  tissue,  and  have  an  epidermis  without 
cuticular  pores.  The  former  two  classes  have  much  in 
common ;  they  have  true  flowers,  woody  tissue  and 
cuticular  pores,  and  hence  may  be  united  into  one  wider 
class,  Vasculares.  But  exogens  and  endogens  are  also 
most  strongly  distinguished.  Exogens  have  a  stem  or 
trunk  consisting  of  distinct  bark,  pith,  and  wood  in  con- 
centric layers,  leaves  with  reticular  veins,  seeds  with  two 
seed-leaves  and  a  naked  radicle  ;  generally  speaking,  too, 
the  parts  of  the  flower  are  some  multiple  of  two  or  five  in 
number.  Endogens,  on  the  contrary,  have  no  distinct 
bark,  pith,  and  wood,  no  concentric  layers,  leaves  with 
parallel  veins,  seeds  with  one  seed-leaf,  and  a  radicle  not 
naked ;  they  have,  too,  the  parts  of  the  flower  generally  a 
multiple  of  three  in  number.  . 

These  are  the  very  widest  classes  in  what  is  called 
the  natural  system  of  botanical  arrangement ;  but  similar 
principles  are  observed  in  all  its  minor  classes.  The 
continual  efforts  of  botanists  are  directed  to  bringing  the 
great  multitudes  of  plants  together  in  species,  genera, 
orders,  classes,  and  in  various  intermediate  groups,  so 
that  the  members  of  each  group  shall  have  the  greatest 
number  of  points  of  mutual  resemblance  and  the  fewest 
points  of  resemblance  to  members  of  other  groups.  Thus 
*s  best  fulfilled  the  great  purpose  of  classification,  which 
reduces  multiplicity  to  unity,  and  enables  us  to  infer  of  «J3 
tfe*  other  mtmben  of  a  clau  what  we  know  of  any  <MM 
member,  provided  we  distinguish  properly  between  those 


XXXIL]  AND  ABSTRACTION.  283 

qualicies  which  are  likely  or  are  known  to  belong  to  the 
class,  and  those  which  are  peculiar  to  the  individual  It 
is  a  necessary  condition  of  correct  classification,  as  re- 
marked by  Prof.  Huxley,  that  the  definition  of  a  group 
shall  hold  exactly  true  of  all  members  of  the  group,  and 
not  of  the  members  of  any  other  group.  To  carry  out  thia 
condition  in  the  natural  sciences  is,  however,  very  difficult, 
because  kinds  of  plants  or  animals  are  continually  dis- 
covered which  stand  in  an  intermediate  position  between 
classes  which  would  otherwise  be  well  distinguished. 
Thus  ferns  much  embarrass  the  fundamental  division  of 
plants,  because  though  they  have  no  true  flowers,  and  in 
this  and  other  respects  agree  with  other  acrogens,  yet 
they  have  abundance  of  woody  fibre,  which  would  entitle 
them  to  rank  with  vascular-es,  the  larger  group  of  which 
exogens  and  endogens  are  the  subdivisions. 

It  may  be  remarked  that  the  progress  of  chemistry  ii 
rapidly  rendering  it  a  science  of  classification  ;  and  in  fact 
the  whole  theory  of  chemical  combination  now  depends 
on  a  correct  grouping  of  elements  and  compounds.  Di 
Roscoe  in  his  Lessons  in  Elementary  Chemistry  enu- 
merates no  less  than  eleven  classes  of  metals,  each  class 
having  a  number  of  properties  in  common.  Thus  the 
metals  of  the  alkalies,  namely,  Potassium,  Sodium,  Caesium, 
Rubidium,  Lithium,  form  a  remarkably  natural  class. 
They  are  all  soft,  easily  fusible,  volatile  at  high  tempera- 
tures ;  they  combine  with  great  force  with  oxygen,  decom- 
pose water  at  all  temperatures,  forming  oxides  which  are 
very  soluble  in  water,  and  become  powerfully  caustic  and 
alkaline  bodies  from  which  water  cannot  be  expelled  by 
heat.  Their  carbonates  are  soluble  in  water,  .and  each 
metal  forms  only  one  compound  with  chlorine. 

The  metals  of  the  alkaline  earths,  Calcium,  Strontium, 
and  Barium,  also  form  a  very  natural  class,  distinguished 
by  the  fact  that  their  carbonates  are  insoluble  in  pure 


284  CLASSIFICATION- 

watei,  but  soluble  in  water  containing  carbonic  acid  ii 
•olution.  The  gold  class  contains  the  rare  or  valuable 
metals  Gold,  Platinum,  Palladium,  Rhodium,  Ruthenium 
Indium,  and  Osmium,  which  are  not  acted  on  by  nitric 
acid,  and  can  only  be  dissolved  by  chlorine  or  the  mixture 
of  acids  called  aqua  regia.  The  oxides  can  be  reducer 
ar  deoxidised  by  simply  heating  them. 

Natural  classifications  give  us  the  deepest  resemblance  i 
and  relations,  and  may  lead  us  ultimately  to  a  knowledge 
of  the  way  in  which  the  varieties  of  thing*  are  produced. 
They  are,  therefore,  essential  to  a  true  science,  and  may 
aknost  be  said  to  constitute  the  framework  of  the  science. 
Yet  it  does  not  follow  that  they  are  appropriate  for  all 
purposes.  When  our  purpose  is  merely  to  recognise  the 
name  of  a  chemical  element,  a  plant  or  an  animal,  its 
character  as  defined  in  a  natural  system  would  give  us 
little  or  no  assistance.  The  chemist  does  not  detect 
potassium  by  getting  it  into  the  state  of  metal,  and  trying 
whether  it  would  decompose  water.  He  merely  observes 
which,  among  all  the  compounds  of  potassium,  have  the 
best  marked  and  most  peculiar  characters  ;  thus  a  com- 
pound of  potassium,  platinum,  and  chlorine  is  most 
distinctive  or  characteristic  of  the  metal,  and  is  generally 
used  as  a  means  of  recognising  it ;  but  a  fine  violet 
colour  which  potash  gives  to  the  flame  of  a  lamp  was 
also  used  as  an  indication  of  its  presence  long  before 
the  spectroscope  was  introduced  to  analyse  such  colours 
An  artificial  classification  of  the  elements  is  thus  ne- 
cessary to  the  detection  of  substances,  and  accordingly 
in  any  book  on  chemical  analysis  will  be  found  arrange 
ments  of  the  elements  according  to  characters  of  verj 
minor  importance,  but  which  are  selected  on  account  ol 
the  ease  and  certainty  with  which  they  can  be  observed. 

In  Botany,  again,  the  natural  system  of  classification  is 
£u  from  being  well  suited  for  determining  the  name  of  a 


JCXXIL]  AND  ABSTRACTION.  285 

plant,  because  the  classes  are  often  defined  by  the  form  oJ 
minute  parts  of  the  seed,  the  arrangement  of  the  seed- 
vessel,  and  other  parts  which  it  is  usually  difficult  or 
sometimes  impossible  to  examine.  Accordingly  botanists 
usually  arrange  their  genera  and  species  in  the  order  of 
the  natural  system,  but  contrive  a  sort  of  key  or  artificial 
arrangement,  in  which  the  most  simple  and  apparent 
characters,  often  called  characteristics,  are  employed  for 
the  discrimination  of  the  plants.  The  best  arrangement 
of  this  kind  as  regards  British  plants  is  to  be  found  in 
Bentham's  British  Flora.  In  reality  the  celebrated 
Lmnaean  arrangement  of  plants  was  intended  by  its 
author  to  serve  in  this  way.  Linnaeus  was  too  profound 
a  philosopher  to  suppose  that  the  numbers  of  stamens 
and  pistils  usually  expressed  the  real  relationships  of 
plants.  Many  of  his  classes  were  really  natural  classes, 
but  the  stamens  and  pistils  were  selected  as  the  general 
guide  to  the  classes  and  orders,  as  being  very  plain  and 
evident  marks. 

Closely  connected  with  the  process  of  classification 
ts  that  of  abstraction.  To  abstract  is  to  separate  the 
qualities  common  to  all  individuals  of  a  group  from  the 
peculiarities  of  each  individual.  The  notion  "  triangle  " 
is  the  result  of  abstraction  in  so  far  as  we  can  reason 
concerning  triangles,  without  any  regard  to  the  particular 
size  or  shape  of  any  one  triangle.  All  classification  Im- 
plies abstraction,  for  in  framing  and  defining  the  class 
1  must  separate  the  common  qualities  from  the  peculiari 
ties.  When  I  abstract,  too,  I  form  a  general  conception, 
or  one  which,  generally  speaking,  embraces  many  objects. 
If,  indeed,  the  quality  abstracted  is  a  peculiar  property  oi 
:he  class,  or  one  which  belongs  to  the  whole  and  not  to 
iny  other  objects,  I  may  not  increase  the  extent  of  the 
notion,  so  that  Mr  Herbert  Spencer  is,  perhaps,  right  in 
holding  that  we  COD  abstract  without  generalizing.  We 


286  CLASSIFICATION,  Ar.  [l 

often  use  this  word  ftneraliiatlon.  and  the  process  may  b€ 
defined  as  inferring  of  a  whole  class  what  we  know  only  o4 
a  part.  Whenever  we  regard  the  qualities  of  a  thing  a« 
lot  confined  to  that  thing  only  but  as  extended  to  otha 
>bjects;  when,  in  fact,  we  consider  a  thing  only  as  a 
member  of  a  class,  we  are  said  to  genermlixe.  If,  aftei 
studying  the  properties  of  the  circle,  we  proceed  to  those 
jf  the  ellipse,  parabola  and  hyperbola,  it  is  soon  found 
that  the  circle  is  only  one  case  of  a  whole  class  of  curves 
called  the  conic  sections,  corresponding  to  equations  o< 
the  second  degree;  and  I  generalize  when  I  regard  cer- 
tain of  the  properties  of  the  circle  as  shared  by  many 
other  curves. 

Dr  Whewell  added  to  the  superabundance  of  terms  to 
express  the  same  processes  when  he  introduced  the  ex- 
pression Colligation  of  ficU.  Whenever  two  things  are 
found  to  have  similar  properties  so  as  to  be  placed  in  the 
same  class  they  may  be  said  to  be  connected  together. 
We  connect  together  the  places  of  a  planet  as  it  moves 
round  the  sun,  when  we  conceive  them  as  points  upon  a 
common  ellipse.  Whenever  we  thus  join  together  pre- 
viously disconnected  facts,  by  a  suitable  general  notion  or 
hypothesis,  we  are  said  to  colligate  them,  Dr  Whewell 
adds  that  the  general  conceptions  employed  must  be 
(i)  clear,  and  (2)  appropriate  ;  but  it  may  well  be  ques- 
tioned whether  there  is  anything  really  different  in  theat 
processes  from  the  general  proceat  of  natural  classifi catioi 
•rhich  we  hare  considered. 


LESSON  XXXIIL 

REQUISITES  OF  A  PHILOSOPHICAL 
LANGUAGE. 

AMONG  the  subsidiary  processes  requisite  to  the  successful 
prosecution  of  inductive  reasoning  must  be  placed  the 
construction  of  a  suitable  language.  It  is  in  fact  impos- 
sible to  over-estimate  the  importance  of  an  accurate  and 
copious  language  in  any  science;  and  the  study  of  things 
would  be  almost  useless  without  names  to  denote  those 
things  and  record  our  observations  concerning  them. 

It  is  easily  apparent,  indeed,  that  language  serves 
three  distinct  and  almost  independent  purposes  :— 

1.  As  a  means  of  communication. 

2.  As  a  mechanical  aid  to  thought 

3.  As  an  instrument  of  record  and  reference. 

In  its  first  origin  language  was  used  chiefly  if  not  exclu- 
sively for  the  first  purpose.  Savage  tribes  exist  in  great 
numbers  at  the  present  day  who  seem  to  accumulate  no 
knowledge.  We  may  even  say  that  the  lower  animals 
often  possess  some  means  of  communication  by  sounds 
or  natural  signs  which  constitute  language  in  the  first 
sense,  though  they  are  incapable  of  reasoning  by  general 
notions. 

Some  philosophers  have  held  that  it  fs  impossible  to 
carry  on  reasoning  without  the  use  of  language.  The 
true  nominalist  went  so  far  as  to  say  that  there  are  no 
such  things  as  general  notions,  and  that  general  names 
therefore  constitute  all  that  is  general  in  science  and 


tSS  REQUISITES   OF  A  [LESt, 

reasoning.  Though  this  is  no  doubt  false  (see  p.  13),  b 
must  nevertheless  be  allowed  that  unless  general  ideas 
were  fixed  and  represented  by  words,  we  could  nevej 
attain  to  sustained  thought  such  as  we  at  present  enjoy 
The  use  of  language  in  the  second  purpose  is  doubtless 
indispensable  in  a  practical  point  of  view,  and  reasoning 
may  almost  be  considered  identical  with  the  correct  us< 
of  words.  When  language  is  used  solely  to  assist  reason- 
ing there  is  no  need  that  the  meaning  of  each  word 
should  be  uxed ;  we  might  use  names,  as  the  letters  x,  y,  *, 
a,  by  c,  &c.,  are  used  in  algebra  to  denote  any  quantity 
that  happens  to  occur  in  a  problem.  All  that  is  requisite 
is  never  to  confuse  the  meaning  attributed  to  a  word  in 
one  argument  with  the  different  meaning  attributed  in 
another  argument  Algebra  may,  in  fact,  be  said  to  con- 
sist of  a  language  of  a  very  perfect  kind  adapted  to  the 
second  purpose  only,  and  capable  of  leading  a  person  to 
the  solution  of  a  problem  in  a  Symbolical  or  mechanical 
manner. 

Language,  as  it  is  furnished  to  us  ready  made  by  the 
habitual  growth  of  centuries,  is  capable  of  fulfilling  all 
three  purposes,  though  by  no  means  in  a  perfect  manner. 
As  words  possess  a  more  or  less  fixed  customary  meaning 
we  can  not  only  reason  by  their  aid,  but  communicate  our 
thoughts  or  record  them  ;  and  it  is  in  this  last  respect  we 
have  now  to  treat  the  subject 

The  multitude  of  facts  required  for  the  establishment 
of  a  science  could  not  be  retained  in  the  memory  witt 
sufficient  accuracy.  Hence  an  indispensable  subsidiar) 
of  induction  is  the  means  of  describing  and  recording  GUI 
observations.  Thus  only  can  knowledge  be  accumulated, 
so  that  each  observer  shall  start  with  the  advantage  oj 
knowing  what  has  been  previously  recorded  and  proved 
It  will  be  necessary  then  to  consider  the  mode  in  which 
language  serves  for  the  registration  of  facts,  and  to  investi 


xxxm.J    PHILOSOPHICAL  LANGUAGE,         289 

gate  the  requisite  qualities  of  a  philosophical  -anguagc 
suitable  to  the  needs  of  science. 

As  an  Instrument  of  record  language  must  evidently 
possets  two  principal  requisites  : 

1.  Precision  or  definiteness  of  meaning. 

2.  Completeness. 

A  name  is  worse  than  useless  unless,  when  used  to 
record  a  fact,  it  enables  MS  to  ascertain  what  was  the 
nature  of  the  fact  recorded.  Accuracy  and  precision  is 
then  a  more  important  quality  of  language  than  abun- 
dance. The  want  of  an  appropriate  word  will  seldom 
give  rise  to  actual  error  and  fallacy ;  it  will  merely  oblige 
us  to  employ  a  circumlocutory  phrase  or  else  leave  the 
fact  unrecorded.  But  it  is  a  self-evident  convenience  that 
whenever  a  thing,  notion,  or  quality  has  often  to  be  refer 
red  to  there  should  be  a  name  appropriated  to  the 
purpose,  and  there  ought  only  to  be  one  name.  Let  us 
consider  in  succession  what  must  be  the  character  of  a 
precise  and  complete  language. 

It  may  not  previously  have  struck  the  reader,  but  it  is 
certainly  true,  that  description  is  impossible  without  the 
assertion  of  resemblance  between  the  fact  described  and 
some  other  fact  We  can  only  describe  a  thing  by  giving 
it  a  name ;  but  how  can  we  learn  the  meaning  of  that 
name  ?  If  we  describe  the  name  by  other  names  we  only 
have  more  names  of  which  the  meanings  are  required, 
We  must  ultimately  learn  the  meanings,  not  from  namei 
but  from  things  which  bear  those  names.  If  anyone 
were  ignorant  of  the  meaning  of  blue  he  could  not  be  in- 
formed but  by  reference  to  something  that  excited  in  him 
the  sensation  of  blueness,  and  had  he  been  blind  from 
birth  he  could  not  acquire  any  notion  of  what  blueness 
was.  There  are  indeed  a  number  of  words  so  familiar 
to  us  from  childhood  that  we  cannot  tell  when  or  how  we 
learnt  their  meanings,  though  it  must  have  been  by  refer 

19 


JOX>  RI*.U,UlSlTt<.S    OF  A  I  LESS 

encc  to  things.  But  when  we  come  to  the  more  precise 
use  of  names  we  soon  have  to  make  fresh  reference  to 
physical  objects.  Then  we  should  describe  the  several 
kinds  of  blue  colour  as  sky-blue,  azure-blue,  indigo- blue, 
cobalt-blue ;  green  colour  we  likewise  distinguish  as  sea- 
green,  olive-green,  emerald-green,  grass-green,  &<x  Th« 
shapes  of  leaves  are  described  in  Botany  by  such  names 
as  ovate,  lanceolate,  linear,  pinnate,  peltate,  referring  the 
mind  respectively  to  an  egg,  a  lance,  a  line,  a  feather, 
and  a  shield.  In  recording  dimensions  it  is  equally  im- 
possible to  avoid  comparison  with  the  dimensions  of 
other  things.  A  yard  or  a  foot  has  no  meaning  unless 
there  be  a  definite  standard  yard  or  foot  which  fixes  its 
meaning ;  and  the  reader  is  probably  aware  that  when  the 
physical  standard  of  a  length  is  once  completely  lost  it 
can  never  be  recovered.  The  word  is  nothing  unless  we 
somewhere  have  the  thing  to  which  it  corresponds. 

The  first  requisite  of  a  philosophical  language  evident- 
ly is  that  "every  general  name  must  have  a  certain  and 
knowable  meaning."  It  need  hardly  be  mentioned  that 
singular  or  proper  names,  the  names  of  distinct  objects, 
must  likewise  be  known;  but  as  such  names  are  merely 
marks  imposed  upon  the  things  they  do  not  need  the 
same  consideration.  General  names  are  a  more  difficult 
-ubject,  because,  as  we  have  seen  in  Lesson  v.,  they  have  a 
louble  meaning  in  denotation  or  extension,  and  connota- 
ion  or  intension.  Of  these  two  meanings  the  connotation 
.s  the  one  which  must  be  fixed;  the  other  cannot  as 
a  general  rule  be  limited  and  defined.  Had  the  narm 
planet  been  restricted  to  Jupiter,  Saturn,  Mars,  Venus, 
and  Mercury,  the  planets  known  before  the  invention  of 
the  telescope,  we  should  have  had  to  find  a  new  name  for 
those  subsequently  discovered,  and  should  even  then 
commit  the  fault  of  calling  by  different  names  those  things 
which  are  closely  similar.  But  if  by  planet  we  mean  any 


xxxili.]    PHILOSOPHICAL  LANGUAGE.        99* 

round  body  revolving  round  the  sun  in  an  orbit  of  slight 
elHpticity,  it  will  include  all  such  bodies  as  may  be  dis 
covered  from  time  to  time,  of  which  more  than  100  art 
already  known.  Similarly  locomotive  engine  is  not  merely 
the  name  of  a  number  of  engines  now  actually  existing ; 
for  if  so  a  new  name  must  be  needed  every  week 
as  some  new  engine  is  made  or  an  old  one  destroyed. 
What  is  fixed  in  a  general  name  is  its  connotation,  or  the 
qualities  implied  in  the  things  bearing  the  name  We 
ought  therefore  as  far  as  possible  to  define  the  meaning 
of  every  general  name  we  use,  not  by  naming  the  objects 
which  it  denotes,  but  the  qualities,  which  it  connotes. 
Having  however  considered  the  subject  of  definition  in 
previous  Lessons  (xii.  and  xm.),  we  need  only  inquire 
here  how  far  it  is  desirable  to  employ  words  which  are 
in  current  use  in  preference  to  newly  invented  terms. 

The  advantage  of  an  old  term  is  that  it  possesses  force 
of  meaning  for  all  persons,  and  so  far  saves  the  necessity 
of  learning  the  meaning  of  a  strange  technical  expression. 
Every  one  knows  what  heat  is,  and  the  expression  scuna 
of  heat  bears  meaning  to  every  person  however  unlearned. 
But  there  is  this  objection  against  old  terms  to  be  noted, 
that  they  are  almost  always  subject  to  ambiguity ;  accord- 
ingly it  will  be  found  that  the  scientific  man  really  uses 
the  word  heat  differently  from  other  persons.  All  things 
are  more  or  less  hot  in  science,  whereas  in  common  life 
we  could  never  say  that  ice  was  hot  or  contained  heat. 
In  fact  heat  means  ordinarily  the  excess  of  temperature 
above  the  ordinary  mean,  and  the  notion  is  purely  relative 
to  that  of  cold.  We  also  apply  the  word  analogously  to 
tensations  of  taste,  as  when  we  say  pepper  is  hot,  oz 
even  to  purely  mental  phenomena,  as  in  a  hot  dispute,  a 
not  temper,  &c.  If  to  avoid  these  ambiguities  we  invent 
a  new  term,  Caloric^  we  may  give  it  any  precision  oi 
meaning  we  like,  but  we  raise  one  more  obstacle  to  the 

19-3 


*92  REQUISITES  OF  A 

study  of  science,  because  there  is  one  more  technical 
term  to  be  learnt 

This  difficulty  is  especially  great  in  the  science  of 
political  economy.  We  there  deal  with  such  familiar 
ideas  as  wealth,  money,  value,  currency,  capital,  labour, 
exchange,  but  it  is  the  very  familiarity  of  the  ideas  which 
occasions  the  greatest  difficulty,  because  different  people 
attach  different  meanings  to  the  words,  and  infinite  logo- 
machy (Greek  \6yos,  word;  fu^i?,  battle),  or  disputes 
arising  on  merely  verbal  questions,  is  the  result.  Even  if 
a  writer  carefully  defines  the  meaning  in  which  he  uses 
those  terms  he  cannot  oblige  other  persons  to  bear  the 
definitions  in  mind.  The  other  alternative  of  inventing 
wholly  new  terms  is  out  of  the  question,  as  it  would  un- 
doubtedly render  a  work  intolerable  to  most  readers. 
The  only  advice  that  can  be  given  is  to  introduce  a  new 
term  where  it  is  likely  to  be  readily  accepted  and  to  dis- 
place an  old  ambiguous  term ;  but  otherwise  to  endeavour 
to  remove  the  ambiguity  of  the  old  term  by  constantly 
keeping  in  view  a.  precise  definition  of  the  intended 
meaning. 

A  complete  philosophical  language  will  be  composed 
of  two  distinct  kinds  of  terms,  which  form  respectively 
the  descriptive  terminology  and  the  nomenclature  of  the 
science. 

A  descriptive  terminology,  as  pointed  out  by  Dr 
Whewell,  must  include  all  the  terms  required  to  describe 
exactly  what  has  been  observed  concerning  any  object  or 
phenomenon,  in  order  that  we  may  possess  a  permanent 
record  of  the  observation.  For  every  quality,  shape, 
circumstance,  degree  or  quantity  there  must  be  an  appro- 
priate name  or  mode  of  expression.  Thus  in  recording 
the  discovery  of  a  new  mineral  we  ought  to  be  able  to  fix 
in  words  its  exact  crystalline  form,  its  colour,  it*  degree 
rf  hardness,  its  specific  gravity,  smell  and  taste  if  any, 


AXXIII.]    PHILOSOPHICAL  LANGUAGE.        293 

and  many  other  qualities  which  may  possess  importance 
Modern  botany  arose  from  the  efforts  of  Linnaeus  to 
create  a  system  of  terms  by  which  every  par*  and 
character  of  a  plant  can  be  accurately  described.  The 
language  of  botany,  as  since  improved,  presents  the  most 
complete  instance  of  a  scientific  terminology.  Geology 
suffers  much,  as  I  apprehend,  from  the  difficulty  of  find- 
ing accurate  terms ;  such  names  as  trap,  basalt,  gneiss, 
granite,  tuff,  greenstone,  trachyte,  porphyry,  lava,  &c., 
are  exceedingly  vague  and  almost  impossible  to  define, 
and  at  the  same  time  to  distinguish.  Where  a  quality 
does  not  admit  of  degree  or  quantity  it  only  requires  a 
single  name ;  otherwise  we  must  find  some  mode  of  exact 
measurement  and  expression.  The  invention  of  any  in 
strument  for  measuring  a  quality  which  has  been  before 
unmeasured  is  always  an  important  step  in  science,  and 
the  construction  of  the  thermometer  by  Fahrenheit  and  the 
pendulum  clock  by  Huyghens  were  great  eras  in  science. 
On  the  other  hand,  each  science  requires  a  nomen- 
clature or  collection  of  names  for  the  distinct  objects  or 
classes  of  objects  treated  in  it  In  mineralogy  the  names 
of  separate  minerals,  such  as  haematite,  topaz,  amphibole, 
epidote,  blende,  polybasite,  form  the  nomenclature ;  in 
chemistry  we  have  all  the  names  of  the  elements,  togetna 
with  a  vast  apparatus  of  names  for  organic  and  other 
compounds,  such  as  ethyl,  acetyl,  cyanogen,  napthalin, 
benzol,  &c.  In  astronomy  the  names  of  the  planets, 
satellites,  nebulae,  constellations  or  individual  stars,  form 
a  nomenclature  of  by  no  means  a  perfect  or  convenient 
load  ;  and  geology  has  similarly  a  nomenclature  neces- 
sarily of  an  incomplete  character,  in  the  Barnes  of  the 
successive  formations,  silurian,  devonian,  carboniferous, 
permian,  triassic,  eocene,  miocene,  pliocene,  post-plio* 
up  fty, 
It  is  evident  that  a  nomenclature  must  possess  name* 


294  REQUISITES  OF  A  J.LKS 

of  various  degrees  of  generality,  including  individual 
objects  if  they  need  separate  record,  mfima  sptcus  \\ 
luch  there  be,  with  wider  classes,  up  to  the  summa 
ftntra,  or  widest  notions  embraced  in  the  science.  In 
astronom)  we  deal  chiefly  with  the  names  of  individuaJ 
objects,  and  there  is  as  yet  but  little  scope  for  classi 
fication.  In  such  natural  sciences  as  botany  or  zoology 
there  is  seldom  or  never  any  need  of  names  for  indi- 
viduals, as  an  indefinite  multitude  of  individuals  generally 
resemble  each  other  very  closely  in  a  great  number  of 
properties,  so  as  to  constitute  what  has  been  called  a 
natural  "«*  Mr  Mill  uses  this  term  to  denote  "  one  of 
those  classes  which  are  distinguished  from  all  others,  not 
by  one  or  a  few  definite  properties,  but  by  an  unknown 
multitude  of  them  ;  the  combination  of  properties  on 
which  the  class  is  grounded  being  a  mere  index  to  an 
indefinite  number  of  other  distinctive  attributes." 

According  to  Mr  Mill's  language  he  seems  to  include 
in  a  nomenclature  only  the  names  of  supposed  species; 
for  he  says : — "A  nomenclature  may  be  defined,  the  collec- 
tion of  names  of  all  kinds  with  which  any  branch  oi 
knowledge  is  conversant  ;  or  more  properly,  of  all  the 
lowest  kinds,  or  infima  species,  those  which  may  be  sub- 
divided indeed,  but  not  into  kinds,  and  which  generally 
accord  with  what  in  natural  history  are  termed  simply 
•pecies."  But  the  fact  is  that  naturalists  have  now  aban- 
doned the  notion  that  the  species  is  any  definite  form ; 
many  species  are  divided  already  into  subspecies  and 
varieties,  or  even  varieties  of  varieties ;  and  according  to 
the  principles  of  Darwin's  theory  the  subdivision  might 
fo  on  indefinitely.  It  is  surely  most  reasonable  to  regard 
the  natural  kingdoms  of  vegetables  and  animals  as  ar- 
ranged in  an  indefinite  series  of  classes  and  subclasses, 
and  all  the  names  attaching  to  any  such  classes  belong 
to  the  nomenclature 


xxxiil.]    PHILOSOPHICAL  LANGUAGE.         29* 

Again,  Mr  Mill  docs  not  include  in  the  nomenclature 
such  general  names  as  denote  conceptions  artificially 
formed  in  the  course  of  induction  and  investigation.  Ac- 
cordingly, besides  a  terminology  suited  for  describing 
nrith  precision  the  individual  facts  observed,  there  is  a 
branch  of  language  containing  "  a  name  for  every  com- 
mon property  of  any  importance  or  interest,  which  we 
detect  by  comparing  those  facts  :  including  (as  the  con- 
cretes corresponding  to  those  abstract  terms)  names  foi 
the  classes  which  we  artificially  construct  in  virtue  oi 
those  properties,  or  as  many  of  them,  at  least,  as  we  have 
frequent  occasion  to  predicate  any  thing  of."  As  exam- 
ples of  this  class  of  names  he  mentions  Circle,  Limit, 
Momentum,  Civilization,  Delegation,  Representation 
While  the  nomenclature  contains  the  names  of  natural 
classes,  this  third  branch  of  language  would  apparently 
contain  the  names  of  artificial  ideas  or  classes. 

But  I  feel  great  difficulty  in  giving  a  clear  account  of 
Mr  Mill's  views  on  this  subject,  and,  as  my  object  in  these 
Lessons  does  not  allow  of  the  discussion  of  unsettled 
questions,  I  must  conclude  by  referring  the  reader  who 
desires  to  continue  the  subject,  to  the  4th  and  6th  chap- 
ters of  the  4th  Book  of  Mr  Mill's  System  of  Logic,  which 
treat  of  the  Requisites  of  a  Philosophical  Language. 

See  Dr  Whewell's  "  Aphorisms  concerning  the  Lan- 
guage of  Science,"  at  the  end  of  his  Philosophy  o) 
the  Inductive  Sciences. 

Thomson's  Outline  of  the  Laws  of  Thought*  con- 
tains most  interesting  remarks  on  the  general  natuit 
and  use  of  Language,  §§  17 — 31. 


QUESTIONS  AND  EXERCISES. 

LESSON  I.— Introduction. 

I.  Wha.  are  the  meanings  of  a  Law  of  Nature,  and  * 

Law  of  Thought  ? 
S.  Explain    the    distinction   between    the    Form    oi 

Thought,  and  the  Matter  of  Thought 

3.  In  what  sense  may  Logic  be  called  the  Science  oi 

Sciences  ? 

4.  What  is  the  derivation  of  the  name  Logic  ? 

5.  How  does  a  Science  differ  from  an  Art,  and  why  is 

Logic  more  in  the  form  of  a  Science  than  an 
Art? 

6.  Can  we  say  that  Logic  is  a  necessary  aid  in  correct 

reasoning,  when  persons  who  have  never  studied 
logic  reason  correctly  ? 

LESSON  \\.-Three  Parts  «f  Logic. 

1.  Name  the  parts  of  which  a  syllogism  is  composed. 

2.  How  far  is  it  correct  to  say  that  Logic  is  concerned 

with  language  ? 

3.  What  are  the  three  acts  of  mind  considered  in 

Logic?    Which  of  them  is  more  especially  the 

subject  of  the  Science  ? 
4-  Can  you  state  exactly  what  is  meant  by  a  general 

notion,  idea,  or  conception  ? 
$•  How   do  the   Nominalists,  Realists,  and  Concep- 

tualists  differ  in  their  opinions  as  to  the  nature 

of  a  general  notion  ? 
S.  What  is  the  supposed  fourth  part  of 


QUESTIONS  AND  EXERCISES.         *9) 
LESSON  III.— Terms. 

»  Define  a  name  or  term. 

2.  What  is  a  categorematic  term  ? 

3.  Explain  the  distinction  between  a  collective  and  a 

general  term. 

4.  Distinguish  the  collective  and  distributive  use  of 
the  word  all  in  the  following  : — 

(1)  Non  omnis  moriar  (i.e.  I  shall  not  all  die). 

(2)  u  All  men  find  their  own  in  all  men's  good, 

And  all  men  join  in  noble  brotherhood." 
Tennyson. 

(3)  Non  omnia  possumus  omnes  (*.  e.  we  cannot  aU 

do  all  things). 

J.  Which  of  the  following  are  abstract  terms  ? 

Act,  ingratitude,  home,  hourly,  homeliness,  intro- 
duction,   individuality,    truth,    true,    trueness, 
yellow,  yellowness,  childhood,  book,  blue,  in- 
tention, reason,  rationality,  reasonableness. 
&  Define  a  negative  term,  and  mention  the  mark  by 
which  you  may  recognise  it. 

7.  Distinguish  a  privative  from  a  negative  term,  and 

find  some  instances  of  privative  terms. 

8.  Describe  the   logical  characters  of  the  following 

terms,  with  the  precautions  given  at  p.  26. 

Metropolis  Consciousness  Sect 

Book  Lord  Chancellor  Nation 

Library  Vegetable  Kingdom  Institution 

Great  Britain  Brilliance  Light 

Caesar  Weight  Observation 

Void  Sensation  Tongue 

Gold  Cesar  Air 

Prime  Minister  Caesarian  Mentor 

IpdigectibUity  Application  Anarchy 

Manchester  Individual  Retribution 

Recollection  Volume  Solemnity 


8          QUESTIONS  AND  EXERCISES. 

Insignificant  Language  Understanding 

Brilliant  Adornment  Geology 

Independence  Agreement  Demeanour 

Heavinesi  Obliquity  Resemblance 

Ulustmtion  Motionless  Departure 

Section  Henry  VIIL  Nestor 

Whiteness  Formal  Logic  Alexander 

LESSON  \\-AmbigHity  of  Terms, 
l    Define  univocal  terms,  and  suggest  some  tenof 

whicu  jure  perfectly  univocaL 
t.  What  are   the  other  names   by  which  equivoca 

terms  are  often  called  ? 

3.  Distinguish  the  three  kinds  of  ambiguous  terms, 

and  find  instances  of  each. 

4.  Distinguish  the  three  causes  by  which  the  third  and 

most  important  class  of  ambiguous  terms  have 
been  produced. 

t  Explain   the   ambiguity  of   any  of  the    following 
terms,  referring  each   to  its  proper  cause,  and 
tracing  out  as  far  as  possible  the  derivation  of 
each  separate  meaning  from  the  original  meaning. 
BUI  Minister  Subject  Letter 

Table  Clerk  Object  Star 

Term  Order  Earth  Pole 

School  Wood  Law  Reason 

Air  Bull  Sensation  Bed 

Glass  Volume  Art  Bowl 

Peer  Scale  Interest  **-»*< 

S«SMe  Feeling  Paper  Diriric* 

Ball  Kind  Bolt  Class 

LESSON  V.—  Twofold  meaning  of  Terms. 
I    Distinguish    very    carefully   the    meanings   in   cm- 

tension  and  intension  of  the  terms — 
Quadruped,  railway,  human  being,  engine,  moo* 
Uin,  Member  of  Parliament 


QUESTIONS  AND  EXERCISES,         299 

»   Enumerate  the   synonyms  or  other   names  used 
instead  of  extension  and  intension. 

3.  According  to  what  law  is  the  quantity  of  extension 

connected  with  the  quantity  of  intension  ?  Show 
that  the  law  holds  true  of  the  following  series  orf 
terms — 

(1)  Iron,  metal,  element,  matter,  substance. 

(2)  Matter,  organized  matter,  animal,  man. 

(3)  Ship,  steamship,  screw -steamship,  iron  screw- 

steamship,  British  iron  screw  steamship. 

(4)  Book,    printed    book,    dictionary,   Latin    die* 

tionary. 

4.  Distinguish    between    the  connotation  and  deno- 

tation of  a  term. 

5.  Select   from  the  list  of  terms  under  Lesson  IIL, 

Question  8  (p.  297),  such  terms  as  are  non-con- 
no  tat  ive  according  to  Mr  Mill's  views. 

6.  Arrange  the  following  terms  in  series  as  in  ques- 

tion 3,  placing  each  term  of  greater  extension 
before  a  term  of  less  extension.  Point  out 
which  are  the  terms  of  greatest  and  least  inten- 
sion in  each  series. 


Emperor 

Animal 

Planet 

Teacher 

Dissenter 

Mammalian 

Baptist 

Individual 

Matter 

Timber 

Jupiter 

Solicitor 

Person 

Ruler 

Quadruped 

Horse 

Organized  substance 

Being 

Heavenly  body 

Lawyer 

Napoleon  III 

Christian 

Alexander 

Episcopalian 

LESSON  VI.— Growth  of  Language. 

I.  Trace  out  the  generalization  or  specialization  whicfe 
has  taken  place  in  any  of  the  following  words :— 


o          QUES77ONS  A  YD  EXEXC/SES. 

Kind,  genus,  class,  species,  order,  rank,  Augusta* 
president,    speaker,    Utopia,    rock,    Commons, 
doctor. 
2.  Point  out  metaphors  derived  from  the  notions  of 

weight,  straightness,  rock,  wind. 
3    Distinguish  as  accurately  as  possible  the  meanings 
of  the  following  synonyms  : — 
Sickness,  malady ;  mud,  mire ;  confutation,  refu- 
tation ;  boundary,  limit ;  mind,  intellect ;  recol- 
lection, reminiscence;   procrastination,  dilato- 
riness  ;  converse,  reverse,  obverse,  inverse, 
4.  Form  lists  of  all  the  words  derived  from  any  of  the 
following  roots  :— • 

(1)  Tendtre,  to  stretch,  as  in  intention,  attention. 

(2)  Pontre,  to  place,  as  in  position,  supposition. 

(3)  Gtnus,  tribe  or  kind,  as  in  genus,  generation. 

(4)  Munus,  gift,  as  in  remuneration,  common  (I .a tin, 

Communis}. 

(5)  Modus,  shape  or  fashion,  as  in  mood,  moderate. 

(6)  Scribere,  to  write,  as  in  scribe,  inscription,  de- 

scribe. 

(7)  Capere  to  take,  as  in  deception,  incipient 

LlSSON  Vll.—Ltibnitx  on  Knowledge. 

I,  What  are  the  characters  of  perfect  knowledge  ? 
l.  Describe  the  character  of  the  knowledge  which  w*» 
have  of  the  following  notions  or  objects : — 

A  syllogism. 

Electricity. 

Motion. 

A  triangle. 

Eternity. 

The  weight  of  the  earth  (5852  trillions  of  toaft 

The  colour  of  the  sky. 


QUESTIONS  AND  EXERCISES.          y* 

£  Explain  exactly  what  you  mean  by  intuitive  know* 
ledge. 

LESSON  VIII.— Propositions. 

1.  Define  a  proposition,  and  name  the  parts  of  which 

it  is  composed. 

2.  How  are  propositions  classified  ? 

3.  Name  the  four  kinds  of  categorical  propositions, 

and  their  symbols. 

4.  Under  which  classes  are  singular  and  indefinite 

propositions  placed  ? 

5.  Enumerate  the  most  usual  signs  of  the  quantity  of 

a  proposition. 

6.  What  are  modal  propositions  according  to  early 

logicians,  and  according  to  Thomson  ? 

7.  How  far  do  logicians  consider  propositions  with 

regard  to  their  truth  or  falsity  ? 

LESSON  IX.— Opposition  of  Propositions. 

i.  State  the  quantity  of  the  subject  and  predicate  in 

each  of  the  propositions  A,  E,  I,  0. 
9.  Select  out  of  the  following  propositions,  pairs  o/ 

contrary,  contradictory,  subaltern*  and  subcoa- 

trary  propositions^— 

(1)  Some  elements  are  known. 

(2)  No  elements  are  known. 

(3)  All  elements  are  known. 

(4)  Not  all  elements  are  known. 

(5)  Some  elements  are  not  known. 

(6)  All  elements  are  not  known. 

j.  What  propositions  are  true,  false,  or  doubtful, 
(i)  when  A  is  false,  (3)  when  I  is  false, 

(a)  when  E  is  false,  (4)  when  0  is  false? 

4.  Prove  by  means  of  the  contradictory  proposition! 


tt         QUESTIONS  AND  EXERCISES. 

that   subcontrary  propositions   cannot   both   bt 
false. 

5.  Show  by  means  of  the  subcontrary  propositions 

that  contrary  propositions  may  both  be  false. 

6.  What  quantity  would    you  assign   to  each  of  tht 

following  propositions  ? 

(1)  Knowledge  is  power. 

(2)  Nebulae  are  material  bodies. 

(3)  Light  is  the  vibration  of  an  ether. 

(4)  Men  are  more  to  be  trusted  than  we  »>»<"fcT 

(5)  The  Chinese  are  industrious. 

7.  Why  it  it  desirable  in  controversy  .,,  retute  a  state- 

ment by  its  contradictory  and  not  by  its  contrary  2 


'  X. — Ctnvtrrie*  **d  Immediate  Inftrtitc*. 

1.  Define  inference  and  conversion. 

2.  What  are  converse  and  convertend  propositions? 
J.  State  the  rules  of  valid  conversion, 

4.  Name  all  the  kinds  of  conversion. 

5.  By  what  process  do  we  pass  from  each  of  tfee  fol- 

lowing propositions  to  the  next  ? 

(1)  No  knowledge  is  useless. 

(2)  No  useless  thing  is  knowledge, 

(3)  All  knowledge  is  noMiseless.        **•         3  '  I 

(4)  All  knowledge  is  useful 

(5)  What  is  not  useful  is  not  knowledge   l 

(6)  What  is  useless  is  not  knowledge,    «- 

(7)  No  knowledge  is  useless. 

&  Gire  the  logical  opposites  of  the  following  prop*   *^  *ft 
sition,  and  the  converse  of  its  contradictory  ?— ^  *\\*~" 
'     *  He  cannot  become  rich  who  will  not  labour." 

p  Apply  negative  conception  to  the  proposition  "  Afi 
men  are  falUble  *  then  convert  and  show  thai  . 
the  result  is  the  contrapositive  of  the  original 


QUESTIONS  AND&XERCISES. 


fc.  Classify  the  propositions  subjoined  into  the  foui 

following  groups: —  ,^y-~~" 

«.  Those  which  can  be  inferred  from  (i).  \*~r 
t.  Those  from  which  (i)  can  be  inferred.  "*r 
c.  Those  which  do  not  contradict  (i),  but 

be  inferred  frem  it 
J.  Those  which  contradict  (i).        p 
(i)  AH  just  acts  are  expedient  acts. 
£    (2)  No  expedient  acts  are  unjust,  - 
*"-£-  (3)  No  Just  acts  a*6  inexpedient 
&,  ^  (4)  All  inexpedient  acts  are  unjust 

(5)  Some  unjust  acts  are  inexpedient 
c)  (6)  No  expedient  acts  are  v*s 

(7)  Some  inexpedient  »CvS  are  unjust 

(8)  All  expedient  acts  are  just 

(9)  No  inexpedient  acts  are  just 
(10)  All  unjust  acts  are  inexpedient 
(n)  Some  inexpedient  acts  are  just  acts. 

(12)  Some  expedient  acts  are  just 

(13)  Some  just  acts  are  expedient 
.•'14)  Some  unjust  acts  are  expedient 

LlSSONS  VIII.  IX.  and  X.— Examples  of  Propotittou. 

The  reader  is  desired  to  ascertain  the  logical  character 
3f  each  of  the  following  propositions;  he  is  to  state  ol 
?ach  whether  it  is  affirmative  or  negative,  universal,  par- 
ticular, singular  or  indefinite,  pure  or  modal,  exclusive  or 
exceptive,  &c. ;  when  irregularly  stated  he  is  to  reduce  the 
proposition  to  the  simple  logical  order;  he  is  then  to 
convert  the  proposition,  and  to  draw  immediate  inference* 
from  it  by  any  process  which  may  be  applicable. 

(1)  All  birds  are  feathered. 

(2)  No  reptiles  are  feathered. 

(l)  Fixed  stars  are  self-luminous. 


QUESTIONS  AND  EXERCISE*. 

(4)  Perfect  happiness  is  impossible. 

(5)  Life  every  man  holds  dear. 

(6)  Every  mistake  is  not  a  proof  of  ignorance. 

(7)  Some  of  the  most  valuable  books  are  seldom  read 

(8)  He  jests  at  scars  who  never  felt  a  wound 

(9)  Heated  metals  are  softened. 

(10)  Not  one  of  the  Greeks  at  Thermopylae  escaped. 

(11)  Few  are  acquainted  with  themselves. 

(12)  Whoso  loveth  instruction  loveth  knowledge, 
'13)  Nothing  is  harmless  that  is  mistaken  for  a  virtue 
^14)  Some  of  our  muscles  act  without  volition. 

(15)  Metals  are  all  good  conductors  of  heat 

(16)  Fame  is  no  plant  that  grows  on  mortal  soil. 

(17)  Only  the  brave  deserve  the  fair. 

(18)  No  one  is  free  who  doth  not  command  himself. 

(19)  Nothing  is  beautiful  except  truth. 

(20)  The  wicked  shall  fall  by  his  own  wickedness. 

(21)  Unsafe  are  all  things  unbecoming. 

(22)  There  is  no  excellent  beauty  that  hath  not  some 

strangeness  in  the  proportion. 

(23)  It  is  a  poor  centre  of  a  man's  actions,  himself. 

(24)  Mercy  but  murders,  pardoning  those  that  mi. 

(25)  I  shall  not  all  die.     (Non  omnis  morutr.) 

(26)  A  regiment  consists  of  two  battalions. 

(27)  Tis  cruelty  to  load  a  falling  man. 

(28)  Every  mistake  is  not  culpable. 

(29)  Quadrupeds  are  vertebrate  anim^ 

(30)  Not  many  of  the  metals  are  brittle. 

(31)  Many  are  the  deserving  men  who  are  unfortunate 
(32;  Amalgams  are  alloys  of  mercury. 

(33)  One  kind  of  metal  at  least  is  liquid. 

(34)  Talents  are  often  misused. 

£35)  Some  parallelograms  have  tAep-  adjoining 
equal 

(36)  Britain  is  an  island. 

(37)  Romulus  and  Remus  were  twins. 


QUESTIONS  AND  EXERCISES.          90$ 

(38)  A  man's  a  num. 

(39)  Heaven  is  all  mercy. 

(<JO)  Every  one  is  a  good  judge  of  his  own  interests. 
(41)  All  parallelograms  have  their  opposite  angles  eqoftV 
(43)  Familiarity  breeds  contempt 

(43)  No  one  is  always  happy. 

(44)  Every  little  makes  a  mickle. 

LESSON  XL— Logical  Analysis  of  StnUnct* 

1.  How  does  the  grammatical  predicate  differ  from  tht 

logical  predicate  ? 

2.  Distinguish  between  a  compound  and  a  complex 

sentence  ;  and  between  coordinate  and  subordinate 
propositions. 

Ji  Enumerate  the  grammatical  expressions  which  may 
form 

(l)  A  subject  (4)  An  object 

(a)  An  attribute.  (5)  An  adverbial 

(3)  A  predicate. 

4.  Examine  the  following  sentences,  ascertain  which 
are  compound  or  complex,  and  point  out  the  co- 
ordinate or  subordinate  propositions. 

(1)  Happy  is  the  man  that  findeth  wisdom,  and  the 

man  that  getteth  understanding. 

(2)  Heat,  being  motion,  can  be  convened  into  me- 

chanical force. 

(3)  Ceres,  Pallas,  Juno,  and  Vesta  are  minor  planets, 

or  asteroids. 

(4)  Knowledge  comes,  but  wisdom  lingers. 

(5)  Fortune  often  sells  to  the  hasty  what  she  give*  sf 

those  who  wait. 
(5)         Thousands  at  His  bidding  speed, 

And  post  o'er  land  and  ocean  without  rest ; 
They  also  serve  who  only  stand  and  wait 

30 


6          QUESTIONS  AND  EXERCISES. 

(7)  Pride  that  dines  on  vanity,  sups  on  contempt 
*l)  Nobody  can  be  healthful  without  exercise,  neithei 

natural  body,  nor  politic. 
(9)  Nature   is   often  hidden,   sometimes   overcome 

seldom  extinguished. 

(10)  It  is  impossible  to  love  and  be  wise. 

(11)  Though  gods  they  were,  as  men  they  died 

(12)  He  that  is  not  industrious  envieth  him  that  is. 

(13)  Ye  are  my  friends,  if  ye  do  whatsoever  I  command 

you. — John  xv.  14. 

(14)  The  wisdom  that  is  from  above  is  first  pure,  then 

peaceable,   gentk,   and   easy  to   be  intreated, 
full   of  mercy,  and  good   fruits,  without  par- 
tiality,  and  without  hypocrisy. — James  iii.  17. 
5.  Analyse  in  the  form  of  a  scheme  or  diagram  any  oi 
the  following  sentences  : — 

(1)  The  first  aphorism  of  Bacon's  Novum  Organum} 

on  p.  229. 

(2)  Some  judgments  are  merely  explanatory  of  their 

subject,  having  for  their  predicate,  a  conception 
which  it  fairly  implies,  to  all  who  know  and  can 
define  its  nature. 

(3)  There  be  none  of  the  affections  which  have  been 

noted  to  fascinate  or  bewitch,  but  love  and 
envy :  they  both  have  vehement  wishes  ;  they 
frame  themselves  readily  into  imaginations  and 
suggestions  ;  and  they  come  easily  into  the  eye, 
especially  upon  the  presence  of  the  objects, 
which  are  the  points  that  conduce  to  fascination 
if  any  such  there  be. 

Further  examples    for   analysis   must  be   sought  ir 
'Jalgleish's  Grammatical  Analysis,  with  Progritm*  Ex- 
(Oliver  and  Boyd.)   Edinburgh,  1866.   Prior  $d 


QUESTIONS  AND  EXERCISES          J0» 
LESSON  XII.— The  Prtdicable^  etc. 

I.  Define  each  of  the  five  predicables. 

S.  In  what  sense  may  we  say  that  the  genus  is  pan  ol 

the  species,  and  in  what  sense  that  the  species  is 

part  of  the  genus  ? 

3.  Select  from  the  terms  in  the  6th  Question  of  Les- 

son v.,  p.  299,  such  as  are  genera,  species, 
highest  genera,  or  lowest  species  of  other  terms. 

4.  Explain  the  expressions  sui  generis,  homogeneous, 

heterogeneous,  summum  genus,  infima  species, 
tree  of  Porphyry. 

5.  Name  a  property  and  accident  of  each  of  the  follow- 

ing classes  : — Circle,  Planet,  Bird,  Member  ol 
Parliament,  Ruminant  Animal. 

6.  What  are  the  rules  of  correct  logical  division. 

7.  The  first  name  in  each  of  the  following  series  ol 

terms  is  that  of  a  class  which  you  are  to  divide 

and  subdivide  so  as  to  include  all  the  subjoined 
minor  classes  in  accordance  with  the  laws  oi 
division. 

H  PtofU.              («)    Trianglt.  (3)    Ruuowng. 

Equiangular  Induction  (Imperfect) 

Alien*                    Isosceles  Deduction 

Naturalized             Right-angled  Mediate  Inference 

Subjects              Scalene  Induction 

Peers                      Obtuse-angled  Hypothetical  Syllogism 

Natural-born  Disjmnctive  Syllogism 

Subjects 
Clergy 
Baronets 
Common 

8.  Divide  any  of  the  following  classes :— Goveranvmtft 

Sciences,  Logical  terms,  Propositions. 

9.  Of  what  does  a  logical  definition  consist  ? 


o6          QUESTfONS  AND  EXERCISES. 

10.  What  are  the  rules  of  correct  definition  ? 

M.  What  rules  do  the  following  definitions  break? 

(1)  Life  is  the  sum  of  the  vital  functions. 

(2)  Genus  is  the  material  part  of  the  species, 

(3)  Illative  conversion  is  that  in  which  the  truth  ol 

the  converse  can  be  inferred  from  that  of  tb< 
convertend. 

(4)  Mineral  substances   are  those  which  have  not 

been  produced  by  the  powers  of  vegetable  01 

animal  life, 
(j)  An  equilateral  triangle  is  a  triangle  whose  sides 

and  angles  are  respectively  equal 
(6)  An  acute-angled  triangle    is  one  which  has  an 

acute  angle. 

LESSON  XIII.— Pascal  and  Descartes  on  Method. 
(l)  What  is  the  use  of  nominal  definitions  ? 
(a)  How  must  we  employ  definitions  in  order  to  avoid 
confusion  ? 

(3)  How  far  can  we  be  said  to  be  free  to  use  any  name 

for  any  object  ? 

(4)  What  according  to  Pascal  is  the  true  method  of 

avoiding  error  ? 

(5)  How  do  we  learn  the  meanings  of  words  which 

cannot  be  defined  ? 

(6)  Give  instances  of  words  which  can  be  dearly  de- 

fined and  of  others  which  cannot 

(7)  State  the  five  rules  of  method  given  in  the  Port 

Royal  Logic. 

(8)  Explain    Descartes'  rules  for  the   attainment  of 

truth. 

LESSON  XIV.— Laws  of  Thought. 
u  State  the  three  Fundamental  Laws  of  Thov.^ht,  and 
apply  them  to  the  following  notions  : — 


QUESTIONS  AND  EXERCISES.         30$ 

(1)  Matter,  organic,  inorganic. 

(2)  Undulations,  polarized,  non-polarixed 

(3)  Figure,  rectilinear,  curvilinear. 

9,  Is  it  wrong  to  assert  that  animal  cannot  both  be 
vertebrate  and  invertebrate,  seeing  that  some 
animals  are  vertebrate  and  some  are  not  ? 

j,  Select  from  the  following  such  terms  as  are  nega- 
tives of  the  others,  and  such  as  are  opposites  :— 
Light,  plenum,  gain,  heat,  decrease,  loss,  darkness, 
cold,  increase,  vacuum. 

4.  How  is  Aristotle's  dictum  applicable  to  the  follow- 
ing arguments? 

(1)  Silver  is  a  good  conductor  of  electricity ;  for  such 

are  all  the  metals. 

(2)  Comets  cannot  be  without  weight ;  for  they  are 

composed  of  matter,  which  is  not  without  weight 

LESSON  XV.—Syibgism:  tht  Rubs. 

1.  Distinguish  mediate  and  immediate  inference. 

2.  Define  syllogism,'  and  state  with  what  it  is  synony- 

mous. 
£  What  are  the  six  principal  and  two  subordinate 

rules  of  the  syllogism  ? 

4.  In  the  following  syllogisms  point  out  in  succession 
the  conclusion,  the  middle  term,  the  major  term, 
the  minor  term,  the  major  premise  and  the  minor 
premise,  observing  this  precise  order, 
(i)  All  men  are  fallible  ; 

All  kings  are  men ; 

A       Therefore  all  kings  are  falHUe.  \ 

/*          \(2)  Platrfcum  is  a  irfetal ;  ^  J 

/4       \^    All  metals  combine  with  oxygen  ;     / 
A       Therefore  Platinum  combines  with  oxygen. 
^ 

P 


fto         QUESTIONS  AND  EXERCISES. 

(3)  Hottentots  are  capable  of  education  ;  for  Hotten- 
tots are  men,  and  ail  men  are  capable  of  edu- 
cation. 

j.  Explain  carefully  what  is  meant  by  non-distribvtxw 
of  the  middle  term. 


LxsiON  XVI.—7*/  Afoods  mnd  Ft£*ru  <f  tk* 
Syllogism. 

1.  Name  the  rules  of  the  syllogism  which  are  broken 

by  any  of  the  following  moods,  no  regard  being 
paid  to  figure  :  — 
AIA,  EEI,  IEA,  101,  HA,  AEI. 

2.  Write  out  all  the  64  moods  of  the  syllogism  and 

strike  out  the  53  invalid  ones. 

3.  Show  in  what  'figures  the  following  premises  give  a 

valid  conclusion  :  —  A  A,  A  I,  E  A,  OA. 
4  In  what  figures  are  I  E  O  and  E  I  O  valid  ? 

5.  To  what  moods  do  the  following  valid  syllogisms 

belong?    Arrange  them  in  correct  logic&l  order. 
(i)  Some  Vs  are  Z's.  (2)  All  Z's  are  Vs. 

No  X's  are  Vs.  No  Y>s  are  X's. 

Some  Z's  are  not  X's.  No  Z's  are  X's. 

(3)  No  fish  suckles  its  young  ; 
The  whale  suckles  its  young  ; 

Therefore  the  whale  is  no  fish. 

6.  Deduce  conclusions  from  the  following  pifmiiM 

and  state  to  what  mood  the  syllogism  belongs. 

(1)  Some  amphibious  animals  are  mammalian. 
All  mammalian  animals  are  vertebrate. 

(2)  All  planets  are  heavenly  bodies. 
No  planets  are  self-luminous. 

(5)  Mammalian  animals  are  quadrupeds. 
No  birds  are  quadrupeds. 

(4)  Ruminant  animals  are  not  predacious. 
The  lion  is  predacious. 


QUESTIONS  AND  EXERCISES.         jn 

jr.  Invent  examples  to  show  that  false  premises  may 

give  true  conclusions. 
8.  Supply  premises  to  the  following  conclusions  :— - 

(1)  Some  logicians  are  not  good  reasoners. 

(2)  The  rings  of  Saturn  are  material  bodies. 

(3)  Party  government  exists  in  every  democracy. 

(4)  All  fixed  stars  obey  the  law  of  gravitation. 

LESSON  XVII.~77k  Syllogism;  Reductum. 

I.  State   and  explain  the  mnemonic  lines  Barbara, 

Celarent,  &c. 

S.  Construct  syllogisms  in  each  of  the  following  moods, 
taking  X,  Y,  Z,  for  the  major,  middle,  and  minor 
terms  respectively,  and  show  how  to  reduce  them 
to  the  first  figure : — 

Cesare,  Festino,  Darapti,  Datisi,  Ferison,  Camenes, 
Fesapo. 

3.  What  is  the  use  of  Reduction  ? 

4.  Prove  that  the  following  premises  cannot  give  a 

universal  conclusion — E  I,  I  A,  O  A,  I E. 

5.  Prove  that  the  third  figure  must  have  an  affirmative 

minor  premise,  and  a  particular  conclusion. 

6.  Reduce  the  moods   Cesare  and  Camenes  by  the 

Indirect  method,  or  Reductio  ad  Impossible. 

LESSON  XVIII.— Irregular  and  Compound  Syllogisms. 

1.  Describe  the  meaning  of  each  of  the  terms — En- 
thymeme,  Prosyllogism,  Episyllogism,  Epichei- 
rema,  Sorites. 

au  Make  an  example  of  a  syllogism  in  which  there  arc 
two  prosyllogisms. 

3.  Construct  a  sorites  of  four  premises  and  resolve  it 

into  distinct  syllogisms. 

4.  What  are  the  rules  to  which  a  sorites  most  conform/ 


i 


SI*          QUESTIONS  AND  EXERCISES. 

$.  Th«  reader  is  requested  to  analyse  the  following 
arguments,  to  detect  those  which  are  false,  and  to 
ascertain  the  rules  of  the  syllogism  which  they 
break ;  if  the  argument  appears  valid  he  is  to 
ascertain  the  figure  and  mood  to  which  it  belongs, 
to  stete  it  in  correct  logical  form,  and  then  if  it  b« 
in  an  imperfect  figure  to  prove  it  by  reduction  to 
the  first  figure.  The  first  six  of  the  examples 
should  be  arranged  both  in  the  extensive  and 
intensive  orders.  ^  _ 

1.  None  but  mortals  are  men.     t»        C^-IA^-CA*^ 
Monarchs  are  nielL  A 

Therefore  inon^rchs  are  mortals.  A 
!/*•  Personal  deformity  is  an  affliction  of  nature. 
Disgrace  is  not  an  affliction  of  nature. 
Therefore  personal  deformity  is  not  disgrace. 

8.  Some  statesmen  are  also  authors ;  for  such  are 
Mr  Gladstone,  Lord  Derby,  Lord  Russell,  and 
Sir  G.  C  Lewis. 

C  This  explosion  must  have  been  occasioned  by  gun- 
powder; for  nothing  else  would  have  possessed 
sufficient  force. 

ft.  Every  man  should  be  moderate;  for  excess  will 
cause  diseasej,:^  ,  dju^^o  -^t«*^^^c* 

i.  Blessed  are  the  mercifuljior  they  shall  obtain 
mercy. 

T.  As  almost  all  the  organs  of  the  body  have  a 
known  use,  the  spleen  must  have  some  use. 

ft   Cogito,  ergo  sum.     (I  think,  therefore  I  exist) 

•.  Some  speculative  men  are  unworthy  of  trust ;  for 
they  are  unwise,  and  no  unwise  man  can  be 
trusted. 

jO.  No  idle  person  can  be  a  successful  writer  of  his- 
tory; therefore  Hume,  Macaulay,  Hallam  and 
Grote  must  have  been  industrious. 


QUESTIONS  AND  EXERCISES.         313 

11.  Who  spareth  the  rod,  hateth  his  child;  the  parent 
who  loveth  his  child  therefore  spareth  not  Uw 
rod. 

11.  Comets  must  consist  of  heavy  matter;  for  other 
wise  they  would  not  obey  the  law  of  gravitation 

IS.  Lithium  is  an  element ;  for  it  is  an  alkali-pro 
ducing  substance,  which  is  a  metal,  which  is 
an  element 

14.  Rational  beings  are  accountable  for  their  actions; 
brutes  not  being  rational,  are  therefore  exempt 
from  responsibility. 

15  A  singular  proposition  is  a  universal  one;  for 
it  applies  to  the  whole  of  its  subject 

It.  Whatever  tends  to  withdraw  the  mind  from  pur- 
suits of  a  low  nature  deserves  to  be  promoted ; 
classical  learning  does  this,  since  it  gives  us 
a  taste  for  intellectual  enjoyments ;  therefore  it 
deserves  to  be  promoted. 

17.  Bacon  was  a  great  lawyer  and  statesman ;  and  as 

he  was  also  a  philosopher,  we  may  infer  that  any 
philosopher  may  be  a  great  lawyer  and  statesman, 

18.  Immoral  companions  should  be  avoided ;  but  some 

immoral  companions  are  intelligent  persons,  so 
that  some  intelligent  persons  should  be  avoided. 

19.  Mathematical    study  undoubtedly   improves    the 

reasoning  powers ;  but,  as  the  study  of  logic  is 
not  mathematical  study,  we  may  infer  that  it  doei 
not  improve  the  reasoning  powers, 
to    Every  candid  man  acknowledges  merit  in  a  rival 
every  learned   man  does  not  do  so;  therefore 
every  learned  man  is  not  candid. 

LESSON  XIX. — Conditional  Argument*. 

I.  What  are  the  kinds  of  conditional  proportion*, 
and  by  what  signs  can  you  recognise  them? 


JI4         QUESTIONS  AND  EXERCISES. 

r  What  are  the  rules  of  the  hypothetical  syllogism  ? 
y,  To  what  categorical  fallacies  do  breaches  of  the» 
rules  correspond? 

4.  Select  from  the  following  such  as  are  valid  argv 

ments,  and  reduce  them  to  the  categorical  form 
explain  the  fallacious  reasoning  in  the  others 

(1)  Rain  has   fallen   if  the  gftrnnl^is   wet;  but  th» 
^~\          ground  is  not  wet ;  therefore  rain  has  not  fallen 

(2)  If  rain  has  fallen,  the  ground  is  wet ;  but  rain  has 

not  fallen ;  therefore  the  ground  is  not  wet. 

(3)  The  ground  is  wet,  if  rain  has  fallen ;  the  ground 

is  wet ;  therefore  rain  has  fallen. 

(4)  If  the  ground  is  wet,  ram  has  fallen  ;  but  rain  has 

fallen ;  therefore  the  ground  is  wet 
N.B.     In   these   as   in  other   logical  examples   the 
student  must  argue  only  from  the  premises,  and  not  from 
any  other  knowledge  of  the  subject-matter. 

5.  Show  that  the  canons  of  syllogism  (p.  121)  may 

be   stated  indifferently   in   the  hypothetical   or 
categorical  form. 

6.  State  the  following  in  the  form  of  a  Disjunctive  01 

Dilcmmatic  argument,  and  name   the  kind  to 
which  it  belongs. 

If  pain  is  severe  it  will  be  brief;  and  if  it  last  long  it 
will  be  slight;  therefore  it  is  to  be  patiently  borne. 

LESSONS  XX.  and  XXI— Fallacies. 

i      Classify  fallacies. 

t.  Explain  the  following  expressions : 
A  dicto  secundum  quid  ad  dictum  simpliciter ;  igno- 
ratio  elenchi ;  argumentum  *d  hominem ;  ar£t> 
mentum  ad  populum  ;  petitio  principii ;  circului 
in  probando;  non  sequitur;  post  hoc  ergc 
propter  hoc 


QUESTIONS  AND  EXERCISES.          ji$ 

j.     What  is  arguing  in  a  circle;  and  what  is  a  qne* 
tion-begging  epithet? 

4.  What  differences  of  meaning  may  be  produced  ta 

the  following  sentence  by  varying  the  accent? 
M  Newton's  discovery  of  gravitation  is  not  generally 
believed   to    have   been  at   all  anticipated  by 
several  philosophers  in  England  and  Holland." 

5.  Point  out  the  misinterpretations  to  which  the  fol- 

lowing sentences  might  be  liable. 
(l)  He  went  to  London  and  then  to  Brighton  by 

the  express  train. 

(l)  Did  you  make  a  long  speech  at  the  meeting? 
(3)  How  much  is  five  times  seven  and  nine? 


MISCELLANEOUS  EXAMPLES. 
LESSONS  IX.  to  XXI. 

(Continued  from  p.  313.) 

The  following  examples  consist  partly  of  true  and 
partly  of  false  arguments.  The  reader  is  requested  to 
treat  them  as  follows  : 

1.  If  the  example  is  not  in  a  simple  and  complete 

logical  form,  to  complete  it  in  the  form  which 
appears  most  appropriate. 

2.  To  ascertain  whether  it  is  a  valid   or  fallacious 

argument 

3.  To  assign  the  exact  name  of  the  argument  or  fal- 

lacy as  the  case  may  be. 

4.  If  a  categorical  syllogism,  to  reduce  it  to  the  first 

figure. 

5.  If  a  hypothetical  syllogism,  to  state  it  in  the  cate 

gorical  form. 

^-^tl.  Elementary  substances  alone  are  metals.     Iron  ii 
a  metal  ;  therefore  it  is  an  elementary  substance 


£,( 
QUESTIONS  AND  EXERCISES.. 

2>  r      A 

To  Athenians  could  have  been  Hdots ;  for  all  thi 
HelJts  were  slaves,  and  all  Athenians  were  free  ' 

St.  Aristoue  must  have  been  a  man  of  extraordinary 
A   $  ^industry;  for  only  such  a  man  could  have  pro 
*          duced  his  works.      vrv4^H*ccxA*    AXV*.  -c^^-^ui- 
•4.  Nothing  is  better  than   wisdom;    dry  bread  is     ' 

better  than  nothing ;  therefore  dry  bread  is  better- 

than  wisdom. 
IB   Pitt  was  not  a  great  and  useful  minister;   for 

though  he  would  have  been  so  had  he  came 

out  Adam  Smith's  doctrines  of  Free  Trade,  he 

did  not  carry  out  those  doctrines. 
St.  Only  the  virtuous  are  truly  noble;  some  who  are 

called  noble  are  not  virtuous;  therefore    some 

who  are  called  noble  are  not  truly  noble. 
ST.  Ireland  is  idle  and  therefore  starves ;  she  starves, 

and  therefore  rebels. 
SS.  No  designing  person  ought  to  be  trusted;  en-     1 

gravers  are  by  profession  designers;  therefore    C.    ^ 

they  ought  not  to  be  trusted. 
SS,  Logic    as   it  was   cultivated   by  the   schoolmen        **'^ 

proved  a  fruitless  study ;  therefore  Logic  as  it  is  ^^^ 

cultivated  at  the  present  day  must  be  a  fruitless     ^  ^*» 

study  likewise. 
ft.  Is  a  stone  a  body?  Yes.    Then  is  not  an  animal 

a  body?    Yes.    Are  you  an  animal  ?    I  think  so.   v    0  ^ 

Ergo,  you  are  a  stone,  being  a  body.— Lucian. 
SI   If  ye  were  Abraham's  children,  ye  would  do  the 

works  of  Abraham. — John  viii.  39. 
SI   He  that  is  of  God  heareth  God's  words :  ye  there 

fore  hear  them  not,  because  ye  are  not  of  GoTI^  \^ 

— John  viil  47. 
99.  Mahomet  was  a  wise  lawgiver;  for  he  studied  the 

character  of  his  people,  Q  y  \  t/  /  \  • 


QUESTIONS  AND  EXERCISES.         317 

•4.  Every  one  desires  virtue,  because  every  one 
desires  happiness. 

15.  His  imbecility  of  character  might  have  been  in- 
ferred from  his  proneness  to  favourites  ;  for  all 
weak  princes  have  this  failing. — De  Morgan. 

St.  He  is  brave  \vho  conquers  his  passions ;  he  who 
resists  temptation  conquers  his  passions;  so  that 
he  who  resists  temptation  is  brave. 

IT  Suicide  is  not  always  to  be  condemned;  for  it  is 
but  voluntary  death,  and  this  has  been  gladly 
embraced  by  many  of  the  greatest  heroes  oV 
antiquity. 

•8.  Since  all  metals  are  elements,  the  most  rare  of  all 
the  metals  must  be  the  most  rare  of  all  (he 
elements. 

tt.  The  express  train  alone  does  not  stop  at  this  sta- 
tion ;  and  as  the  last  train  did  not  stop  it  must 
have  been  the  express  train. 

40.  Peel's  remission  of  taxes  was  beneficial ;  the  taxes 

remitted  by  Peel  were  indirect;  therefore  the 
remission  of  indirect  taxes  is  beneficial 

41.  Books  are  a  source  both  of  instruction  and  amuse- 

ment ;  a  table  of  logarithms  is  a  book ;  there- 
fore it  is  a  source  both  of  instruction  and  amuse* 
inert. 

41.  All  desires  are  not  blameable ;  all  desires  are  liable 
to  excess ;  therefore  some  things  liable  to  excess 
are  not  blameable. 

41  Whosoever  intentionally  kills  another  should  suffer 
death ;  a  soldier,  therefore,  who  kills  his  enemy 
should  suffer  death. 

44.  Projectors  are  unfit  to  be  trusted;  this  man  has 
formed  a  project;  therefore  he  is  unfit  to  be 
trusted. 

4A.  Few  towns  in  the  United  Kingdom  have  more  thai 


i*          QUESTIONS  AND  EXERCISES. 

300,000  inhabitants ;  and  as  all  such  towns  ought 
to  be  represented  by  three  members  in  Parlia- 
ment, it  i?  evident  that  few  towns  ought  to  hav« 
three  representatives. 

*4.  All  the  works  of  Shakspeare  cannot  be  read  in 
a  day;  therefore  the  play  of  Hamlet,  being  on« 
of  the  works  of  Shakspeare,  cannot  be  read  ir 
a  day. 

«T.  In  moral  matters  we  cannot  stand  still ;  therefore 
he  who  does  not  go  forward  is  sure  to  fall  behind. 

*8.  The  people  of  the  country  are  suffering  from  famine ; 
and  as  you  are  one  of  the  people  of  the  country 
you  must  be  suffering  from  famine. 

*9.  Those  substances  which  are  lighter  than  water 
can  float  upon  it ;  those  metals  which  can  float 
upon  it  are  potassium,  sodium,  lithium,  &c. ; 
therefore  potassium,  sodium,  lithium,  &c.,  are 
lighter  than  water. 

60.  The  laws  of  nature  must  be  ascertained  by  De- 

duction, Traduction  or  Induction ;  but  the  former 
two  are  insufficient  for  the  purpose ;  therefore 
the  laws  of  nature  must  be  ascertained  by  In- 
duction. 

61.  A  successful  author  must  be  either  very  industrious 

or  very  talented ;  Gibbon  was  very  industrious, 
therefore  he  was  not  very  talented. 

62.  You  are  not  what  I  am ;  I  am  a  man ;  therefore 

you  are  not  a  man. 

•t  The  holder  of  some  shares  in  a  lottery  is  sure  to 
gain  a  prize ;  and  as  I  am  the  holder  of  somi 
shares  in  a  lottery  I  am  sure  to  gain  a  prize. 

•t.  Gold  and  silver  are  wealth ;  and  therefore  the 
diminution  of  the  gold  and  silver  in  the  country 
by  exportation  is  the  diminution  of  the  wealth 
of  the  country. 


QUESTIONS  AND  EXERCISES.          319 

M.  Over  credulous  persons  ought  never  to  be  believed 
and  as  the  Ancient  Historians  were  in  man) 
instances  over  credulous  they  ought  never  to  bi 
believed. 

It,  Some  mineral  compounds  are  not  decomposed  by 
heat ;  all  organic  substances  are  decomposed  b> 
heat ;  therefore  no  organic  substances  are  mi- 
neral compounds. 

5T.  Whatever  schools  exclude  religion  are  irreligious , 
Non-sectarian  schools  do  not  allow  the  teaching 
of  religious  creeds ;  therefore  they  are  irreligious. 

58.  Night  must  be  the  cause  of  day ;  for  it  invariably 

precedes  it. 

59.  The  ancient  Greeks  produced  the  greatest  master- 

pieces of  eloquence  and  philosophy ;  the  Lace- 
daemonians were  ancient  Greeks  ;  therefore  they 
produced  the  greatest  masterpieces  of  eloquence 
and  philosophy. 

•0.  All  presuming  men  are  contemptible;  this  man, 
therefore,  is  contemptible  ;  for  he  presumes  to 
believe  his  opinions  are  correct. 

•1.  If  a  substance  is  solid  it  possesses  elasticity,  and 
so  also  it  does  if  it  be  liquid  or  gaseous ;  but  all 
•substances  are  either  solid,  liquid  or  gaseous; 
therefore  all  substances  possess  elasticity. 

II  If  Parr's  life  pills  are  of  any  value  those  who  take 
them  will  improve  in  health  ;  now  my  friend  who 
has  been  taking  them  ha«  improved  in  health  j 
therefore  they  are  of  value. 

•t.  He  who  calls  you  a  man  speaks  truly  ;  ne  who  calli 
you  a  fool  calls  you  a  man ;  therefore  he  who 
calls  you  a  fool  speaks  truly. 

•4.  Who  is  most  hungry  eats  most ;  who  eats  least  is 
most  hungry ;  therefore  who  eats  least  eats  most 

W.  What  produces  intoxication  should  be  prohibited  j 


310         QUESTIONS  SiND  EXERCISES. 

the  use  of  spirituous  liquors  causes  intoxication 
therefore  the  use  of  spirituous  liquors  should  be 
prohibited. 

•f .  What  we  eat  grew  in  the  fields ;  loaves  of  bread 
are  what  we  eat ;  therefore  loaves  of  bread  grew 
in  the  fields. 

•  /.  If  light  consisted  of  material  particles  it  would 
possess  momentum  ;  it  cannot  therefore  consist 
of  material  particles,  for  it  does  not  possess 
momentum. 

18  Everything  is  allowed  by  law  which  is  morally 
right ;  indulgence  in  pleasures  is  allowed  by  law ; 
therefore  indulgence  in  pleasures  is  morally  right. 

•t.  AH  the  trees  in  the  park  make  a  thick  shade ;  this 
is  one  of  them,  therefore  this  tree  makes  a  thick 
shade* 

TO.  All  visible  bodies  shine  by  their  own  or  by  re- 
flected Hght.  The  moon  does  not  shine  by  its 
own,  therefore  it  shines  by  reflected  light ;  but 
the  sun  shines  by  its  own  light,  therefore  it  canncx 
shine  by  reflected  light 

Tl.  Honesty  deserves  reward ;  and  a  negro  is  a  fellow- 
creature  ;  therefore,  an  honest  negro  is  a  fellow- 
creature  deserving  of  reward. 

Tl.  Nearly  all  the  satellites  revolve  round  their  planet! 
from  west  to  east ;  the  moon  is  a  satellite;  there- 
fore it  revolves  round  its  planet  from  west  to  east 

Tl.  Italy  is  a  Catholic  country  and  abounds  in  beg 
gars;  France  is  also  a  Catholic  country,  and 
therefore  abounds  in  beggars. 

ft.  Every  law  is  either  useless  or  it  occasions  hurt  U 
some  person  ;  now  a  law  that  is  useless  ought  to 
be  abolished  ;  and  so  ought  every  law  that  occa- 
sions hurt;  therefore  every  law  ought  to  bi 
abolished. 


QUESTIONS  AND  EXERCISES.         jai 

ff.  The  end  of  a  thing  is  its  perfection ;  death  is  the 
end  of  life ;  therefore  death  is  the  perfection  oi 
life. 

ft  When  we  hear  that  all  the  righteous  people  are 
happy,  it  is  hard  to  avoid  exclaiming,  What !  are 
all  the  unhappy  persons  we  see  to  be  thought 
unrighteous? 

f  T.  I  am  offered  a  sum  of  money  to  assist  this  person 
in  gaining  the  office  he  desires;  to  assist  a 
person  is  to  do  him  good,  and  no  rule  of  morality 
forbids  the  doing  of  good ;  therefore  no  rule  oi 
morality  forbids  me  to  receive  the  sum  of  money 
for  assisting  the  person. 

TS.  Ruminant  animals  are  those  which  have  cloven 
feet,  and  they  usually  have  horns;  the  extinct 
animal  which  left  this  foot-print  had  a  cloven 
foot;  therefore  it  was  a  ruminant  animal  and 
had  horns.  Again,  as  no  beasts  of  prey  are  rumi- 
nant animals  it  cannot  have  been  a  beast  of  prey 

Tt.  We  must  either  gratify  our  vicious  propensities, 
or  resist  them;  the  former  course  will  involve 
us  in  sin  and  misery;  the  latter  requires  self- 
denial;  therefore  we  must  either  fall  into  sin 
and  misery  or  practise  self-denial. 

ft.  The  stonemasons  are  benefited  by  the  masons' 
union ;  the  bricklayers  by  the  bricklayers'  union ; 
the  hatmakers  by  the  hatmakers'  union;  in 
short,  every  trade  by  its  own  union ;  therefore 
it  is  evident  that  if  all  workmen  had  unions  all 
workmen  would  be  benefitted  thereby. 

•L  Every  moral  aim  requires  the  rational  means  of 
attaining  it ;  these  means  are  the  establishment 
of  laws ;  and  as  happiness  is  the  moral  aim  of 
man  it  follows  that  the  attainment  of  happ 
requires  the  establishment  of  laws. 

ai 


|22          QUESTIONS  AND  EXERCISES. 

83  He  that  can  swim  needs  not  despair  to  fly ;  for  tc 
swim  is  to  fly  in  a  grosser  fluid,  and  to  fly  is  to 
swim  in  a  subtler. 

St.  The  Helvetii,  if  they  went  through  the  country  of 
the  Sequani,  were  sure  to  meet  with  various 
difficulties ;  and  if  they  went  through  the  Roman 
province,  they  were  exposed  to  the  danger  of 
opposition  from  Caesar;  but  they  were  obliged 
to  go  one  way  or  the  other ;  therefore  they  were 
cither  sure  of  meeting  with  various  difficulties, 
or  exposed  to  the  danger  of  opposition  from 
Caesar.— De  Bello  Gallico,  lib.  I.  6. 

84.  Riches  are  for  spending,  and  spending  for  honour 

and  good  actions;  therefore  extraordinary  ex 
pense  must  be  limited  by  the  worth  of  the  occa- 
sion.— Bacon. 

85.  If  light  is  not  refracted  near  the  surface  of  the 

moon,  there  cannot  be  any  twilight;  but  if  the 
moon  has  no  atmosphere  light  is  not  refracted 
near  its  surface;  therefore  if  the  moon  has  no 
atmosphere  there  cannot  be  any  twilight 

%i  The  preservation  of  society  requires  exchange; 
whatever  requires  exchange  requires  equitable 
valuation  of  property ;  this  requires  the  adoption 
of  a  common  measure ;  hence  the  preservation 
of  society  requires  the  adoption  of  a  common 
measure. 

87  The  several  species  of  brutes  being  created  to 
prey  upon  one  another  proves  that  the  human 
species  were  intended  to  prey  upon  them. 
The  more  correct  the  logic,  the  more  certainly 
the  conclusion  will  be  wrong  if  the  premises  are 
false.  Therefore  where  the  premises  are  wholly 
uncertain,  the  best  logician  is  the  'east  safo 
guide. 


QUESTIONS  AND  EXERCISES.          333 

8».  If  our  rulers  could  be  trusted  always  to  look  to 
the  best  interests  of  their  subjects,  monarchy 
would  be  the  best  form  of  government ;  but 
they  cannot  be  trusted;  therefore  monarchy  is 
not  the  best  form  of  government 

30,  If  men  were  prudent,  they  would  act  morally  for 
their  own  good ;  if  benevolent,  for  the  good  oi 
others.  But  many  men  will  not  act  morally, 
cither  for  their  own  good,  or  that  of  others  ;  such 
men,  therefore,  are  not  prudent  or  benevolent. 

01.  He  who  bears  arms  at  the  command  of  the  magis- 
trate does  what  is  lawful  for  a  Christian;  the 
Swiss  in  the  French  service,  and  the  British  in 
the  American  service,  bore  arms  at  the  command 
of  the  magistrate  ;  therefore  they  did  what  was 
lawful  for  a  Christian.—  Whately. 

W.  A  man  that  hath  no  virtue  in  himself  ever  envieth 
virtue  in  others ;  for  men's  minds  will  either  feed 
upon  their  own  good  or  upon  others'  evil ;  and 
who  wanteth  the  one  will  prey  upon  the  other. — 
Bacon. 

98.  The  object  of  war  is  durable  peace;  therefore 
soldiers  are  the  best  peace-makers. 

94.  Confidence  in  promises  is  essential  to  the  inter- 
course of  human  life  ;  for  without  it  the  greatest 
part  of  our  conduct  would  proceed  upon  chance. 
But  there  could  be  no  confidence  in  promises,  if 
men  were  not  obliged  to  perform  chem ;  the  obli- 
gation, therefore,  to  perform  promises  is  essential 
to  the  same  ends  and  in  the  same  degree. 
If  the  majority  of  those  who  use  public-houses 
are  prepared  to  close  them,  legislation  is  unne- 
cessary ;  but  if  they  are  not  prepared  for  such  a 
measure,  then  to  force  it  on  them  by  outside 
pressure  is  both  dangerous  and  unjust. 

fl— a 


t*4          QUESTIONS  AND  EXERCISES. 

f «.  He  who  believes  himself  to  be  always  in  the  rigL, 
in  his  opinion,  lays  claim  to  infallibility  ;  you 
always  believe  yourself  to  be  in  the  right  in  you: 
opinion ;  therefore  you  lay  claim  to  infallibility 
—  Whately. 

tT.  If  we  never  find  skins  except  as  the  teguments  of 
animals,  we  may  safely  conclude  that  animals 
cannot  exist  without  skins.  If  colour  cannot 
exist  by  itself,  it  follows  that  neither  can  any- 
thing that  is  coloured  exist  without  colour.  So, 
if  language  without  thought  is  unreal,  thought 
without  language  must  also  be  so. 

••.  No  soldiers  should  be  brought  into  the  field  who 
are  not  well  qualified  to  perform  their  part ;  none 
but  veterans  are  well  qualified  to  perform  their 
part;  therefore  none  but  veterans  should  be 
brought  into  the  field. —  Whately. 

ft.  The  minimum  visibile  is  the  least  magnitude  which 
can  be  seen ;  no  part  of  it  alone  is  visible,  and 
yet  all  parts  of  it  must  affect  the  mind  in  order 
that  it  may  be  visible  ;  therefore,  every  part  of 
it  must  affect  the  mind  without  being  visible. 
lOf.  The  scarlet  poppy  belongs  to  the  genus  Papaver, 
of  the  natural  order  Papaveraceae ;  which  again 
is  part  of  the  subclass  Thalamiflorae,  belonging 
to  the  great  class  of  Dicotyledons,  Hence  the 
scarlet  poppy  is  one  of  the  Dicotyledons. 
til  Improbable  events  happen  almost  every  day  ;  but 
what  happens  almost  every  day  is  a  very  pro- 
bable event ;  therefore  improbable  events  art 
very  probable  events. —  Whately. 

UtSSON  XXI 1.— Quantification  of  the  PrtduaU. 
What  does  the  quantification  of  the  predicate  mean! 


QUESTIONS  AND  EXERCISES.          335 

S.  Assign  to  each  of  the  following  propositions  ttt 
proper  symbol,  and  the  symbol  of  its  converse  • 

(1)  Knowledge  is  power. 

(2)  Some  rectangles  are  all  squares. 

(3)  Only  the  honest  ultimately  prosper. 

(4)  Princes  have  but  their  titles  for  their  glories. 

(5)  In  man  there  is  nothing  great  but  mind. 

(6)  The  end  of  philosophy  is  the  detection  of  unity, 
j.  Draw  all  the  contrapositive  propositions  and  imme- 
diate inferences  you  can  from  the  following  pro- 
positions : — 

(1)  London  is  a  great  city. 

(2)  London  is  the  capital  of  England. 

(3)  All  ruminant  animals  are  all  cloven-footed  ani- 

mals. 

(4)  Some  members  of  parliament  are  all  the  minis- 

ters. 

4.  Write  out  in  Hamilton's  notation  the  moods  Baroko 

Darapti,  Felapton,  Bokardo. 

LESSON  XXIII.— BooUs  System  of  Logic. 
I.  Apply  this  system  of  inference  to  prove  the  syl- 
logisms on  p.  141,  in  Cesare,  and  Camestres. 

5.  Show  that  if  all  A's  are  not  B's,  then  no  ffs  art 

A's  ;  and  that  if  all  A's  are  all  B's,  then  all  not 

jfs  are  all  not  ffs. 
V  Develope  the  term  substance,  as  regards  the  tenm 

vegetable,  animal,  organic;  then  select  the  com* 

binations  which  agree  with  these  premises : 
"  What  is  vegetable  is  not  animal  but  is  or- 
ganic ;  what  is  animal  is  organic." 
¥  Test  the  validity  of  this  argument :  "  Good  always 

triumphs,  and  vice  always  fails  ;   therefore  the 

victor  cannot  be   wrong,  nor  *he  vanquished 

right." 


16          QUESTIONS  AND  EXERCISES. 

5.  It  is  known  of  a  certain  class  of  things  that — 
(l)  Where  the  quality  A  is,  B  is  not. 
(a)  Where  B  is,  and  only  where  B  is,  C  and  D  are 
What   can  we  infer  from  these  premises  ol 
the  class  of  things  in  which  A  is  not  pre- 
sent but  C  is  present  ? 

4  II  all  X's  are  ^s;  all  £*s  are  C's;  all  Cs  are  /7s 
shew  that  all  X's  are  /7s,  and  that  all  not  /7s  are 
not  X's. 

LESSON  XXIV.— Method. 

I.  What  is  the  supposed  position  of  method  accord- 
ing to  former  logical  writers,  and  what  are  the 
rules  of  method? 

a.  Explain  the  expressions  ncbis  notiora,  and  notion* 
natures. 

3.  Of  what  kind  is  the  usual  method  of  instruction  ? 

4.  Prove  that  analysis  in  extension  is  synthesis  in  in-; 

tension,  using  some  of  the  series  of  terms  in 
Question  6,  Lesson  V.  as  illustrations. 

5.  Explain  the  exact  meanings  of  the  expressions  L 

priori  and  a  posteriori  knowledge. 

6.  To  which  kind  belongs  our  knowledge  of  the  fol- 

lowing facts  ? 
(i)  The   light  of  the  stars  takes   a   long  time  to 

reach  us. 

(a)  Vaccination  is  a  preservative  against  small-pox 
(5)  A  meteor  becomes  heated  in  passing  through  the 

air. 
(4]  There  must  be  either  some  inhabitants  or  TM 

inhabitants  upon  Jupiter. 

LESSON  XXV.— Perfect  Induction. 

k  Define  and  distinguish  Deduction,  Induction,  and 
Traduction. 


QUESTIONS  AND  EXERCISES.          31} 

2.  Find  an  instance  of  reasoning  in  Traduction. 
^.  Distinguish  Perfect  and  Imperfect  Induction. 

4.  How  does  Mr  Mill  define  Induction,  and  what  if 

his  opinion  of  Imperfect  Induction? 

5.  What  is  the  use  of  Perfect  Induction? 

6  Construct  some  instances  of  the  inauctive  syllo- 
gism, and  show  that  they  may  be  thrown  into  a 
disjunctive  form. 

LESSON  XXVI.— Induction,  Analogy  and  ExampU. 

X.  From  what  circumstance  arises  the  certainty  and 
generality  of  reasoning  in  geometry? 

2.  Find  other  instances  of  certain  and  general  reason* 

ing  concerning  the  properties  of  numbers. 

3.  Why  are  inductive  conclusions  concerning  prime 

numbers  uncertain  and  not  general? 

4.  Why  is  a  single  instance  sometimes  sufficient  to 

warrant  a  universal  conclusion,  while  in  other  cases 
the  greatest  possible  number  of  concurring  in- 
stances, without  any  exception,  is  not  sufficient  to 
warrant  such  a  conclusion? 

5.  What  are  the  strict  and  ordinary  meanings  of  the 

word  analogy? 

6.  Explain  the  use  of  Examples. 

7.  Explain  exactly  the  difference  between  analogical 

argument  and  ordinary  induction. 

LESSON  XXVll.—Ohtrvatum  and  Experiment. 

I.  What   is    the  false    method  of   Science    against 

which  Bacon  protested? 
a.  Explain  the  exact  meaning  of  Bacon's  assertions, 

that  man  is  the  Servant  and  Interpreter  of  Nature, 

and  that  Knowledge  is  Power. 
j,  How  does  experiment  differ  from  observation? 


|28          QUESTIONS  AND  EXERCISES. 

4.  Classify  the   sciences   according  as   they   empto) 

passive  observation,  expenment,  or  both. 

5.  Name  the   chief  points   in  whir.h   experiment  is 

superior  to  mere  observation. 

6   What  is  the  principal  precaution  needful  in  obser- 
vation ? 

7.  Explain  how  it  is  possible  to  anticipate  nature  an  j 
yet  establish  all  conclusions  upon  the  results  of 
experience. 

LESSONS  XXVI 1 1.  and  XXIX.— Methods  of  Induction. 

1.  Define  exactly  what  is  meant  by  a  cause  of  an 

event,  and  distinguish  cause,  occasion,  antece- 
dent. 

2.  Point  out  all  the  causes  concerned  in  the  following 

phenomena : 

(1)  The  burning  of  a  fire. 

(2)  The  ordinary  growth  of  vegetables. 

(3)  The  cracking  of  a  glass  by  hot  water. 

3.  State  and  explain  in  your  own  words  Mr  Mill's 

first  three  Canons  of  Inductive  Method. 

4.  Point  out  exactly  how  the  Joint   Method  differs 

from  the  simple  Method  of  Difference. 

5.  Give  some  instances  of  simple  experiments  fulfil* 

ling  completely  the  conditions  of  the  Method  ol 
Difference. 

i  What  can  you  infer  from  the  following  instance!? 
Antecedents.     Consequents. 

ABDE stqp 

BCD qsr 

BFG vq* 

ADE    tsf 

HK  ^r?w 

ABFG 

ABE ~....f 


QUESTIONS  AND  EXERCISES.          329 

f.  (l)  Friction  alters  the  temperature  of  the  bodies 
rubbed  together. 

(2)  The  sun  is  supposed  to  move  through  space. 

(3)  A  ray  of  light  passing  into  or  out  of  a  dense 

medium  is  deflected. 

Point  out  the  successive  questions  which  would 
have  to  be  decided  in  the  investigation  of  the 
above  phenomena. 

8.  Find  some  simple  instances  of  the  homogeneous 

and  heterogeneous  intermixture  of  effects,  and 
of  the  methods  of  concomitant  variations  and 
residues. 

9.  Since  1842  there  has  been  a  great  reform  of  the 

British  tariff,  and  a  great  increase  of  British 
trade.  Does  this  coincidence  prove  that  the 
first  circumstance  is  the  cause  of  the  second? 
JO.  Supposing  us  to  be  unacquainted  with  the  causes  of 
the  following  phenomena,  by  what  methods 
should  we  investigate  each  ? 

(1)  The  connection  between  the  barometer  and  the 

weather. 

(2)  A  person  poisoned  at  a  meal 

(3)  The  connection  between  the  hands  of  a  clock. 

(4)  The  effect  of  the  Gulf-stream  upon  the  climate  oi 

Great  Britain. 


LESSON  XXX.— Empirical  and  Deductive  Mttkods 

1.  Define  Empirical  Law,  and  find  a  few  additional 

instances  of  such  laws. 

2.  What  are  the  three  steps  of  the  Deductive  Method  / 

3.  Trace  some  of  the  successive  steps  in  the  progress 

of  the  theory  of  gravitation,  showing  that  it  was 
established  by  this  method. 


QUESTIONS  AND  EXERCISES 

LESSON  XXXI.— Explanation,  Ac. 
..    What  do  you  mean  by  the  explanation  of  a  fact  ? 
1.  State  the  three  ways  in  which  a  law  of  nature  maj 

be  explained,  and  suggest  some  additional  in* 

stances  of  each  case. 
j,  Define  tendency.    Do  all  causes  consist  only  of 

tendencies,  or  can  you  find  examples  to  the  con- 
trary? 
f.  Give  a  definition  of  hypothesis.     How  may  a  valid 

be  distinguished  from  an  invalid  hypothesis  ? 
f.  What  place  does  hypothesis  hold  in  the  Deductive 

Method? 

6.  Explain  the  ambiguities  of  the  words  theory  and 
fact. 

LESSON  XXXII.— Classification 

i.  Define  classification,  and  give  the  derivation  of  the 

word. 
i.  What  do  you  mean  by  important  characters  in 

classification  ? 

3.  State  Dr  Whewell's  criterion  of  a  good  natural 

arrangement 

4.  Distinguish  between  a  natural  and  artificial  system 

of  classification. 

5.  What  do  you  mean  by  a  characteristic  quality  ?    Is 

it  always  an  important  quality  ? 

6.  Define  abstraction,  generalization,  and  colligation 

of  facts. 

7.  What  are  the  characters  of  a  notion  properly  ab» 

tracted? 

LlSSON   XXXIII.— Requisites  of  a  Philosophical 

Language. 

L  What  are  the  three  purposes  for   which   we   use 
language? 


QUESTIONS  AND  EXERCISES.         331 

ft.  What  are  the  two  chief  requisites  of  a  philosophical 
language  ? 

3.  By  what  considerations  should  we  be  guided  in 

choosing  between  a  new  and  old  scientific  term? 

4.  Distinguish  a  Descriptive  Terminology  and  a  No- 

menclature ;  separate  the  following  terms  ac- 
cording as  they  belong  to  one  or  the  other:— 
Rose,  Rosaceae,  Rose-like,  Potassium,  Alkaloid, 
Ruminant  Animal,  Ruminating,  Ruby,  Ruoy  red 
£  What  does  Mr  Mill  mean  by  the  expression  N» 
tall  Kind? 


INDEX, 


4*D    OONCISI    VOCABULARY    OF    LOGICAL    AND 
TERMS. 


Abacus,  the  logical,  190 

abucissio  Infiniti  (the  cutting 
off  of  the  infinite  or  negative  part,, 
the  process  by  which  we  determine 
the  position  of  an  object  in  a  system 
of  classes,  by  successive  comparison 
and  rejection  of  those  classes  to  which 
it  does  not  belong. 

Absolute  terms,  i.t.  non-relative 
terms,  25  ;  sometimes  used  as  name 
of  non-connotative  terms,  41 

Abstract  terms,  ao,  43 

Abstraction,  a8< 

Accent,  fallacy  of,  174 

accident,  fallacy  of,  176  ;  toe  pre- 
di  cable,  103 

Accidental  definition  is  a  defi- 
nition which  assigns  the  properties 
of  a  species,  or  the  accidents  of  an 
individual  ;  it  is  more  commonly 
called  a  Dttcription. 

Acquired  perceptions.  236 

Added  determinants,  inference 


by,  86 
Adeq 


, 

equate  knowledge,  56 
A  dicto  secundnm  quid,  fcc., 

fallacy  of,  176 
Adjectives,  ai 
Adverbial*,  93 
Affirmative  proposition*,  63 
Algebraic  reasoning,  58,  aig 
Ambiguity  of  all,  to  ;  of  MM/,  70 

of  many  old  terms,  t^i  ;  of  term*  In 

Political  Economy,  292 
Ambiguous  middle  term,  190,  171 
Amphibology,  fallacy  of,  IT* 
Ampliative  proportion*.  6g 
Analogue,    a  thing  analogous  to 

VMIH.  other  thing. 
analysis,  method  <*  M* 


Analogy,  the  cause  of  ambiguity 
35,  50 ;  reasoning  by,  326—8 

Analytics,  (rw  AjwAvruti,)  the  titli 
given  in  the  second  century  to  por- 
tions of  the  Organon,  or  LogicaJ 
Treatises  of  Aristotle ;  they  were 
distinguished  as  the  Prior  and  Pos- 
terior Analytics. 

Analytic  syllogism,  a  syllogism 
in  which  the  conclusion  is  placed 
first,  the  premises  followirf  as  the 
reasons.  See  Synthttit.  ^ylkgism 
the  distinction  is  unimportant 

Antecedent,  of  a  hypothetical  pit 
position,  160  ;  of  an  event,  340 

Anticipation  of  nature,  239 

Antinomy  (d^rl,  against ;  Kopos, 
law),  the  opposition  of  one  law  or  roll 
to  another.  Kant. 

A  posteriori  knowledge,  aot 

A  priori  knowledge,  208 

Arbor  Porphyriana,  see  Trtt  of 

Porphyry. 

Argument,  (Latin,  a*?iu,  from 
tipybc,  clear,  manifest,)  the  process  ol 
reasoning,  the  shewing  or  proving 
that  which  is  doubtful  by  that  whicfi 
is  known.  See  Inference.  The  mid- 
dle term  of  a  syllogism  is  sometime! 
called  specially  the  argument. 

Argumentum  a  fortiori,  an 
argument  in  which  we  prove  thai 
the  case  in  question  is  more  strouf 
or  probable  than  one  already  aon- 
ceded  to  be  sufficiently  so. 

Argnmentnm  ad  hominem, 
178 

Argnmentnm  ad  Judiciuao, 
'  to  the  common  MOM  « 


INDEX. 


333 


Argnmenttun  ad  ignoranti- 

Canons  of  syllogism,  121—2;  Hamil 

am,  an  argument  founded  MI  the 
ignorance  of  adversaries. 

ton's  supreme  Canon,  189 
Canons  of  Mill's  Inductive  Methods, 

Ar&omentum   ad  populum, 

First,  340  ;  Second,  242  ;  Third,  945; 

179 

Fourth,  252;  Fifth,  249 

Argnmentum    ad     verecun- 
diam,  an  appeal  to  our  respect  for 

Categorematic  words,  18 
Categorical  propositions,  63 

some  great  authority. 

Categories,  the  ntmm*  ffttfra,  at 

Ajg-umentu-m   ex  concesso, 

most  extensive  classes  into    whack 

a  proof  derived  from  a  proposition 

things  can  be  distributed  ;  they  an 

already  conceded. 

ten  in  number,  as  follows  : 

Aristotle's  Dicta,  123 

Ovo-ia,  Substance  ;  Hwrov,  Quan- 

Art and  Science,  distinction  of,  7 

tity  ;  notov,  Quality  ;  Hpd«  n,  Re- 

Artificial Classification,  284 

lation  ;    ttottlv,    Action  ;    Ud<r\<ivt 

Assertion,  (ad,  to;  tero,  to  Join,) 
a  statement  or  proposition,  affirma- 

Passion, or  suffering  ;   IIov,  Place  ; 
n«re,    Time  ;    Kcttrfeu,    Position  ; 

tive  or  negative. 

*BY«U>,  Habit  or  condition. 

Association  of  ideas,   (cusocia,  to 
accompany;   socius,   a    companion,) 

Everything  which  can  be  affirmed 
must  come  under  one  or  other  of  these 

the  natural   connection  existing   in 

highest  predicates,  which  were  de- 

the mind  between  impressions  which 

scribed  in  the  first  treatise  of  Aris- 

have previously  coexisted,  or  which 

totle's  Orfanon,  called  the  Catego- 

are similar.    Any  idea  tends  to  bring 

ries. 

into  the  mind  its  associated  ideas,  in 
accordance  with  the  two  great  laws 

Cause,  meaning  of,  239 
Aristotle  distinguished  four  kind* 

of  association,   the  Law  of   Conti- 

of causes  for  the  existence  of  a  thing 

guity,  and  the  Law  of  Similarity. 

—i.  The  Material  Cause,  the  sub- 

Assumption, (assumo,  to  take  for 

stance  or  matter  composing  it  ;    2. 

granted,)  any  proposition  taken  as 
the  basis  of  argument  ;  in  a  special 

The  Formal  Cause,  the  pattern,  type 
or  design,  according  to  which  it  is 

sense,  the  minor  premise  of  a  cate- 

shaped ;  3.  The  Efficient  Cause,  the 

gorical  syllogism. 
Attribute,    (attribuo,   to    £ive   or 

force   employed    in    shaping  it  ;    4. 
The  Final  Cause,  the  end,  motive 

ascribe  to,)  a  quality  or  circumstance 
which  may  be  affirmed  (or  denied) 

or  purpose  of  the  work. 
Chance,   ignorance   of   the    causes 

of  a  thing;  opposed  to  Sttbstance^ 
which  see. 

which  are  in  action  ;  see  Probability. 
Character,  derivation  of  the  word, 

Attribute  in  grammar,  92 

46 

Attributive  term,  i.  e.  ConntUtivt 

Characteristics,  385 

CirculUS  in  definiendo,  no,  114 

Axiom,  defininition  of,  1*5 

Ctrculus  in  probando,  179 
Clearness  of  knowledge,  54 

Baconian   method,   955;    Philoso- 

Cognition,   (cognosce,    to    know,) 

phy.  229 

knowledge,  or  the  action  of  mind  i* 

Barbara,  Celarent,  &c.,  145 
Begging  the  Question,  179 

acquiring  knowledge. 
Colligation  of  Facts,  Dr  WhewelTi 

Belief,   assent  to  a  proposition,  ad- 

expression for  the  mental  union  at 

mitting  of  any  degree  of  strength, 
from  the  slightest  probability  to  the 
fullest  certainty  ;  see  Probability. 

facts  by  some  suitable  conception, 
see  286 
Collective  terms,  19 

Bentham,  George,  new  system  of 

Combined  or  complete  method  oi 

Logic,  187 
Boole,  George,  his  system  of  Logic, 
«QI,    hi*  Laws   of  Thought,    197; 
kis  logical  works,  201 

investigation,  258 
Comparison,  'com,  together;  far, 
equal  or  like,    the  action  of  mind  bj 
which  we  judge  whether  two  object* 

334 


INDEX. 


of  thought  are  the  same  or  different        Coixseq  nence  ,  th*  connection  D& 
in  certain  points.     See  Judgment.                twetc    antecedent  and  consequent 
Compatible  terms  are  those  which,            but  often  cued  ambiguously  for  tfa* 

»hough  distinct,  are  not   contradic-            Utter 

jory,  and  Gin  therefore  be  affirmed        Consequent  of  a  hypothetical  pro 

of  the  same  subject  ;  as  "  large  "  and    '        position,  161 
"  heavy  ;  "    "  bright-coloured  "   and    |    Consequent  or  effect  of  a  caow 

"  nauseous."                                                        240 

Jomplex  conception,  inference 
by,  87 
Soviplex  sentence,  91  ;    syllogism, 

Consequent,  fallacy  of  the,  181 
Conservation  of  energy,  963,  269 
Consilience    of    Inductions,    toe 

158 

agreement     of    inductions    derived 

Composition    of  Causes,  the 

from  different  and  independent  seriei 

principle  which  is  exemplified  in  all 
cases  in  which  the  joint  effect  of 

of  facts,  as  when  we  learn  the  mo- 
tion of  the  earth  by  entirely  different 

several  causes  :s  identical  with  the 

modes  of  observation  and  reasoning. 

sum  of  their  separate  effects.     J.  S. 

Whtwell. 

Mill.     See  pp.  253.  265 
Composition,  fallacy  of,  173 

Consistency  of  propositions,  78 
Consistent  terms,  see  cam^atiiU 

Compound  sentence,  90 

terms. 

Comprehension  of  terms,  see  /«- 

faMMK 

Computation,  127 

Contingent,  [conti*g»,  to  touch,) 
that  which  may  or  may  not  happen  ; 
opposed  to  the  necessary  and  im- 

Concept,  that  which  is  conceived, 
the  result  of  the  act  of  conception  ; 

possible. 
Contingent  matter,  80 

nearly  synonymous  with  general  no- 

Continuity, Law  of,  the  principle 

tion,  idea,  thought. 

that  nothing  can  pass  from  one  ex- 

Conception (ctm,  together;  <*/*», 
to  take).   An  ambiguous  term,  mean- 

treme   to  another  without    passing 
through  all  the  intermediate  degrees; 

ing  properly  the  action  of  mind  in 
which  it  takes  several  things  toge- 

motion, for  instance,  cannot  be  instan- 
taneously produced  or  destroyed. 

ther,  so  as  to  form  a  general  notion  ; 

Contradiction,  Law  of,  117,  193 

or  again,  in  which  it  forms  "  a  men- 

Contradictory  terms,    24,    1x9; 

tal  image  of  the  several  attributes 

propositions.  76 

given  in  any  word  or  combination  of 

Contraposition,   conversion   by, 

words."    Mtuutl. 

83,  1  86 

Conceptualists,  13 
Conclusion  of  syllogism,  15,  x»j; 
weakened,  140 
Concrete  terns,  so 

Converse  fallacy  of  accident,  17* 
Conversion  of  propositions,  82  —  85  ; 
with  quantified  predicate,  184 
Convertend,  82 

Conditional  propositions,  62,  160 
Confusion    of    words,    ambiguity 

Coordinate  propositions,  90 
Copula,  16 

from,  31 
Conjugate  words,  those  which  come 

Corollary,  a  proposition  which  fol- 
lows immediately  from  another  which 

from    the    same   root  or  stock,   as 

has  been  proveoL 

ktumm^  k*f**H£,  knrwt*glyt  know- 

Correction of  observations,  253 

ledge. 

Correlative  terms.  a< 

Connotation   of  terms,    30,    41  ;       Criterion  V^-nioioV.  from  KIKVW.  to 

ought  to  be  exactly  fixed,  990 
Consciousness,    the    immediate 

judge),  any  fact,   rule,   knowledge, 
or  means  requisite  to  the  formation 

knowledge  which  the  mind  kas  of 

of  a  judgment  which  shall  decide  a 

its  sensations  and  thoughts,  and,  in 

doubtful  question. 

general,  of  all  its  present  operation*. 
RfuL 

Cross  division,  105 

Ooa*e«tary  «  CoroOwy. 

Data,  {plural  of  datum,  that  wMct 

INDEX. 


is  given, )  the  facts  or  assertions  from 
which  an  inference  is  to  be  drawn. 
Deduction  and  Induction,  212 
Deductive    or    combined  method, 

258,  272 

De  facto,  what  actually  or  really 
happens :  opposed  to  dt  jure,  what 
ought  to  happen  by  law  or  right. 
Definition,  the  logical  process,  109, 

1 1«  ;  of  logic,  i 

Degree,  terms  expressing,  24;  ques- 
tions of,  120 

Demonstration,  (demonstr*,  to 
point  out,)  strictly  the  pointing  out 
the  connection  between  premises  and 
conclusion.  The  t«rm  is  more  ge- 
nerally used  for  any  argument  or 
reasoning  regarded  as  proving  an 
asserted  conclusion.  A  demonstra- 
tion is  either  Direct  or  Indirect.  In 
the  latter  case  we  prove  the  conclu- 
sion by  disproving  Us  contradictory, 
or  she  wing  that  the  conclusion  cannot 
be  supposed  untrue. 
Demonstrative  Induction,  220 
Do  Morgan's  logical  discoveries 

and  writings,  100 
Denotation  of  terms,  39 
Depth  of  a  notion,  see  Intension, 
Derivatives   from   the   root  tftc, 

sight,  52 

Descartes  on  Method,  116,  220 
Description,  vet  Accidental  Defi- 
nition. 

Descriptive  terminology*  *& 
Destructive  dilemma,  168;  hypo- 
thetical syllogism,  162—4 
Desynonymization  of  terms,  49 
Determination,  the  distinguishing 
of  parts  of  a  genus  by  reunion  of  the 
genus  and  difference.    See  Division. 
Development  of  a  teim,  193 
Diagrams,  of  sentences,  93 — 7  ;  of 
syllogisms,    129—133,    142;  of  pro- 
positions, 72 — 75 

Dialectic  («W»A«XTUOI  -n*vq,  the  art 
of  discourse,  from  atoAey«r#«u,  to 
discourse).  The  original  name  of 
Logic,  perhaps  invented  by  Plato; 
ako  used  to  denote  the  Logic  of 
Probable  Matter  (Aristotle),  the 
light  use  of  Reason  and  Language, 
the  Science  of  Beiag;  >t  it  tfaua 
highly  ambiguous  term. 
Dichotomy,  division  by,  107, 193 


Dicta  de  omnl  et  nuDo,  123 

Difference,  the  predicabU,  99 

Differentiation  of  terms,  49 

Dilemma,  167 

Disbelief,  the  state  of  nind  in  whicl 
we  are  fully  persuaded  that  som< 
opinion  is  not  true.  J.  S.  Mill.  Ii 
is  equivalent  to  belief  it.  the  contra 
dictory  opinion  or  assertion,  and  i> 
not  to  be  confused  with  Dvi*bt,  wind 
see. 

Discourse,  or  reasoning,  15 

Discovery,  method  of,  202 

Disjunctive,  propositions,  62,  160; 
syllogism,  166,  194 

Distinct  knowledge,  55 

Distribution  of  terms,  19,  74— 3, 
82,  129 

Division,  logical,  105  ;  metaphysical 
108 ;  fallacy  of,  174 

Doubt,  (dubito,  to  go  two  ways,)  the 
state  of  mind  in  which  we  hesitate 
between  two  or  more  inconsistent 
opinions.  See  Disbelief. 

Drift  of  a  proposition,  the  varying 
meaning  which  may  be  attributed  to 
the  same  sentence  according  to  ac- 
centuation. See  Fallacy  of  accent, 
174—5 


the  doctrine  of  those  who  consider 
that  all  knowledge  is  derived  merely 
from  experience. 

Empirical  Law,  156 

Enthymeme,  153 

Epicheirema,  155 

Episyllogism,  155 

Equivocal  terms,  29 

Equivocation,  30;  causes  of,  31; 
fallacy  of,  171 

Essence,  (gssentia,  from  ftse,  to  be,; 
"  the  very  being  of  anything,  where- 
by it  is  what  it  is."  Locks.  It  is  an 
ancient  scholastic  word,  which  can 
not  be  really  defined,  and  should  b* 
banished  from  use. 

Essential  propositions,  68 

Euler's  diagrams.  72 — 5,  129 — 133, 
142 

Evidence.  (/,  and  vtdtrt,  to  see, 
literally  th*  seeing  of  anything 
The  word  now  means  any  facts  ap- 
prehended by  the  mind  and  mad« 
the  ground*  of  knowledge  and  belief 


INDEX. 


Examples,  use  of,  **j 
Exceptive  proportion*.  68 
Excluded   middle,  law  of,  117, 

119,  192 

Exclusive  proposition*,  68 
Exhaustive  division,  107,  192 
Experience,  228 
Experimentum  crucis,  an  ex- 
periment which  decides  between  two 
rival  theories,  and  shews  which  is  to 
be  adopted,  as  a  finger-post  shews 
which  of  two  roads  is  to  be  taken. 
Explanation,  of  facts,  364 ;  of  laws, 

265 

Explicative  propositions,  68 
Exposita,  a  proposition  given  to  be 

treated  by  some  logical  process. 
Extension  and  intension,  37,  *o8 
Extensive  Syllogism,  159 
Extremes  of  a  proposition,  are  its 
ends  or  terms,  the  subject  and  predi- 


Fact,  175 

Fallacy,  purely  logical,  170;  semi- 
logical,  170 — 175  ;  material,  176 — 
182 ;  in  hypothetical  syllogism,  i6a  ; 
in  dilemma,  168 

False  causa,  fallacy  of,  181 

False  propositions,  70 

Figure  of  speech,  fallacy  of,  175 

Figures  of  the  syllogism,  138 ;  their 
uses,  143 

Form  and  matter  of  thought,  A 

Fundaxnentum  divisionisjios 

Fundamentum  relation!  a,  the 
ground  of  relation,  i.e.  the  series  of 
events  or  circumstances  which  es- 
tablish a  relation  between  two  cor- 
relative terms. 

Fundamental  principles  of  syllo- 
gism, 121 

Gtalenian,  or  41*  figure  of  the  syl- 
logism, 145 

Seneral  notions,  43  ;  terms.  18 
Generalization,  286 ;  of  TJL»*S. 

Generic  property,  102 
3enu»,  98  :  gencralissimum,  too 
Geometrical    reasoning  jS,   ti8; 

Pascal  on,  115 
Grammatical  predicate,  88  ;  »•• 

tence,  89 
Gravitation,  theory  of,  «6c 


tation,  187 

ichel, 


I    Hamilton,  Sir  W.    Method  rf  No 


Herschel,    Sir  ]  ,  on  active 

passive  observation,  234 
Heterogeneous,   101  ; 

ture  of  effects,  252 
Homogeneous,  101 ;  intermktmt 

of  effects,  253,  265 
Homologue,  whatever  is  kernel* 


Homo 


fomology,  a  special  term  for  tha 
analogy  existing  between  parts  of 
different  plants  and  animals,  as  be- 
tween the  wing  of  a  bird  and  the 
fore  leg  of  a  quadruped,  or  between 
the  scales  of  a  fish  and  the  feathers 
of  a  bird. 

Homonymous  terms,  30 

Hypothesis,  269,  270 

Hypothetical  propositions,  6»,x6o, 
syllogism,  161 — a 

Idea  (i£«'a,  fUoc,  image),  a  term  used 
ambiguously,  but  generally  equiva- 
lent to  thought,  notion,  concept 
Defined  by  Locke  as  "Phantasm 
notion,  species,  or  whatever  it  is 
which  the  mind  can  be  employed 
about  in  thinking."  To  have  an  id*a 
of  a  thing  is  to  think  of  that  thing. 

Identity,  kw  of,  117—8 

Idol  (clftwAor,  «l£of,  image),  Bacou's 
figurative  name  for  the  sources  of 
error ;  he  enumerated  four  kinds ; 
Idols  of  the  Tribe,  which  affect  all 
people  ;  Idols  of  the  Cave,  which  are 
peculiar  to  an  individual  ;  of  the 
Forum,  which  arise  in  the  inter- 
course of  mem  ;  of  the  Theatre,  which 
proceed  from  the  systems  of  philoso- 
phers. 

Ignoratio  Elenohi,  178 

Illation  (iliatum,  past  particrpl*  of 
i*Jero,  to  bring  ini.  See  Inftrntc*. 

Illative,  that  which  can  be  inferred. 

Illicit  process,  »(  the  minor  tors, 
131  ;  of  the  major  teem,  13*,  139 

Immediate  inference,  83—7 

Imperfect  figures  of  the  syllo 
gism,  145 

Imperfect  Induction,  913 

Impossible  matter,  80 
Inconsistent  terms  imply  qualitiei 
which  cannot    coexist   ia   the   taxM 


INDEX. 


337 


Inconsistent  propositions,  74 
Indefinite  propositions,  65 
Indefinite  or  infinite  term,  is  a  ne- 

Leibnitz on  Knowledge,  53 
Lemma   (Xa^di/w,   to  take  or  a» 
sume),     a     proposition,    a    premis* 

gative   term   which  only  marks  an 

granted  ;  in  geometry,  a  preliminary 

object  by  exclusion  from  a  class. 
tn  design  ate  propositions.    See  In- 

proposition. 
Limitation,  conversion  by,  82,  87 

definite  propositions. 

Logic,  derivation  of  name,  6 

Indirect    demonstration.     See  De- 

Logical abacus,  slate  and  machine^ 

monstration. 

199 

indirect  inference,  method  of, 

Logomachy,  29* 

Indirect  reduction  of  the  syllo- 

Lowest specie*,  100 

gism,  146,  148  —  9. 

Miachine,  the  logical,  199 

Individual,  what  cannot  be  divided 
without  losing  its  name  and  distinc- 

Major, term,  128  ;  premise,  129 
Many  questions,  fallacy  of,  x8s 

tive    qualities,    although    generally 
capable  of  physical  division  or  par- 

Material fallacies,  170,  176 
Mathematical  induction,  220 

tition,  which  see. 

Matter  of  thought,  4  ;  of  proposi- 

Induction, 212 

tions,  80 

Inductive  syllogism,  211,  214 
Inference,  defined,  8x  ;  immediate, 

Matter  is  defined  by  J.  S.  Mill  as 
"  the  external  cause    to  which  w» 

85  —  87  ;  mediate,  126 

ascribe  our  sensations,"   or  as  Per- 

Infima species,  xoo 

manent  Possibility  of  Sensation. 

Innate  ideas,  see  a  priori  trutks,*<& 

Mediate  inference,  126 

Inseparable  accident,  103 
Instances,  use  of,  227 

Membra    dividentia,  the  parts 
into  which  a  class  is  divided;  tk« 

Intension  and  extension  of  terms, 

constituent  species  of  a  genus. 

37,  99,  208  ;  law  of  relation,  40 
Intensive  syllogism,  159 

Metaphor,  50 
Metaphysical  division,  108 

Intention,  first  and  second,  a  dis- 
tinction between  terms  thus  defined 

Metaphysics  (ra  fxrra  ra  <J>v<Ti*a}1 
the    works  of    Aristotle   which  fol- 

by Hobbes  :—  "  Of  the  first  inten- 

lowed   or    were    studied    after   hii 

tion  are  the  names  *f  things,  a  man, 

Physics.     First  Philosophy,  or  th« 

stone,  &c.  ;    of  the  second  are  the 

so-called  science  of  things  in  their 

names  of  names,  and  speeches,  as 

own  nature  ;  ontology  or  the  scienc* 

universal,  particular,  genus,  species. 

of  Being. 

nllogism,  and  the  like."    A  term  of 

Method    (/j.e'0oJoc,    p.era  and  o£6f. 

the  second  intention  expresses  the 

way),    mode,  way  or  instrument  ol 

mode  in  which  the  mind  regards  or 

accomplishing  an  end. 

classifies  those  of  the  first  intention. 

Method,   the  fourth  part  of  logic, 

Intermediate  link,  explanation 

15,  2oz  ;  Pascal  on,  1x4;  Descartes' 

by,   267 

Discourse  on,  116;  of  indirect  infer- 

Intuitive knowledge,  57 
Inversion  of  subject  and  predicate, 

ence,  192 
Methods  of  Induction,  Agreement, 

67 

240;    Difference,    242;     of    Expert 

Irrelevant  conclusion,   fallacy  of, 

ment,     243,     Joint    Method,    245. 

178 

Residues,  252;  Concomitant  Varia- 

tions, 249 

f  ndgment,  xa 

BXetonymy  (fxerei,  and  ovopi.a,naine) 

grammatical   name   for  the  transfer 

Language,  the  subject  of  logic,  to 

of  meaning  of  a  word  to  a  closely 

banffuage,    requisites    of   philoso- 

connected thing,  as  when  we  speak 

phical,  20o  ;  three  purposes  of,  387 

of  the  church,  meaning  the  people  ii 

Laws  of  thought,  i,  1x7;  of  nature, 

it     See  Transfer  of  meaning. 

139 

BSiddle  Term,  126,  128 

S3* 


INDEX. 


MflUr  J.  S.,  oo  Connotaiive  terms, 
«i  an  Induction,  214  ,  on  Analogy 
uid  Induction,  aa? ;  on  Observation, 
,15  on  Terminology  and  Nomen- 
clature, 994 
ijnor  term,  126;  premise,  129 

daemonic  verses,  Barbara,  &a, 

flodal  proposition,  69,  91 
rlodus,  pitumt  161  ;  tolUns,  i6a 
flodus,   ponendo  tolltnj,    166;  /W- 

&Wo  ponens,   166 

Moods  of  the  syllogism,  136;  ac- 
cording to  Hamilton,  188 

Name,  or  term,  17 

Natural  Classification,  a8o 

Natural  Kinds,  294 

Necessary  matter,  80 

Necessity  (ru,  not ;  and  cesso,  to 
cease),  that  which  always  is  and  can- 
not but  be. 

Negation,  conversion  by,  83 

Negative,  terms,  aa;  propositions, 
°3.  83 ,  premises,  fallacy  of,  133 — 4 

Newton's  experiments,  253,  259 

Nomenclature,  293 

Nominal  definitions,  112 

Nominalists,  13 

Non  causa  pro  causa,  181 

Non  sequitur,  181 

Notion  (fuiscff,  to  know),  the  action 
of  apprehending  or  taking  note  of 
the  various  qualities  of  an  object ;  or 
more  commonly  the  result  of  that 
action.  See  Id* a,  Concept. 

Notiora  naturae,  204 

If  ovum  Organum,  first  aphor- 
isms of,  229 

Numerically  definite  syllogism, 
190 

Object  of  verb,  93 

Objective,   that  which  belongs  to 

the  object  of  thought,  the  Kon-ego; 

opposed   to  Subjective,  which    see. 
Obscure  knowledge,  54 
Observation,  231,  235 
Occasion  of  an  event,  the  proximate 

cause,   or   last    condition    which    is 

requisite  to  bring  other  causes  into 

action .  239 

Opposite  terms,  24,  119 
Opposition  of  propositions,  78 
Org anon  (oaymror,  Latin  Organum, 


instrument),  a  name  for  Mn 
logical  treatises,  first  generally  used 
in  the  tt,th  century,  implying  that 
they  may  be  regarded  as  an  iastru 
ment  to  assist  the  mind.  The  nanv 
was  adopted  by  Bacon  for  his  Nnmm 
Organum. 

Paradox  (vo^d,  U£o,  contrary  U 
opiuion),  an  assertion  contrary  to 
common  opinion,  and  which  may  or 
may  not  prove  true ;  often  wrongly 
used  to  mean  what  U  seif-contradio 
tory  and  absurd. 

Paralogism  (va^aAov^Mu,  to  rea- 
son wrongly),  a  purely  logical  fallacy, 
cc  breach  of  the  rules  of  deductive 


logic. 
Parity  < 


used  'to  denote  that  when  one  case 
has  been  demonstrated,  other  simi- 
lar cases  <*-=»"  be  demonstrated  by  a 
'ike  course  of  reasoning. 

Parenymous  words,  see  O*/M- 

ga±4  words. 

Particular  propositions,  63 — 6,72,79 
Particular  premises,  fallacy  of,  135. 

Partition  or  physical  division,  108 
Per  accidens,  conversion,  82 
Perfect  Figure  of  the  Syllogism, 

145 
Perfect  knowledge,  character* 

of,  53 

Periodic  changes,  250 

Peripatetic  Philosophy  (irtpnraT«», 
to  walk  about),  the  name  usually 
given  to  the  doctrines  of  Aristotle 
and  his  followers,  who  are-  said  to 
have  carried  on  their  studies  and 
discussions  while  walking  about  the 
halls  and  promenades  of  the  Lyceum. 

Fetitio  Principil,  179 

Phenomenon,  240 

Pliilosophical  language,  re- 
quisites of,  200 

Physical  definition  assigns  the 
parts  into  which  a  thing  \n»-  be 
separated  by  partition  or  physical 

Plurative  propositions,  191 
Polylemma,  an  argument  or-  the 
same  form  as  a  dilemma,  bat  in  "hicf 
there  are  more  than  two  alternatives 
Porphyry,  tree  of,  103 


INDEX. 


Port  Royal  Logic,  xxx,  157 
Positive  terms,  22 
Post  hoc,  ergo  propter  hoe, 
iti 

OStulate  (postulatum,  a  thing  de- 
manded ,  a  proposition  which  is  ne- 
cessarily demanded  as  a  basis  of  ar- 
gument ;  in  geometry,  the  postulates 
define  the  practical  conditions  re- 
quired 

Predicables,  98 

Predicaments 
what  can  be  predicated),  see  Cate- 

i*redicate,  62,  88,  92;  quantified, 

Premise,  or  Premiss,  15,  127 

Primary  Laws  of  Thought,  117 

Principle  (printipiumt  beginning), 
the  first  source  of  anything;  some- 
times specially  used  to  mean  the 
major  premise  of  a  syllogism. 

Privative  conception,  inference 
by,  85 

Privative  terms,  24 

Probability,  quantity  or  degree  of 
belief,  or  more  truly,  quantity  of  in- 
formation concerning  an  uncertain 
event,  measured  by  the  ratio  of  the 
number  of  cases  favourable  to  the 
event  to  the  total  number  of  cases 
which  are  possible. 

Probability,  of  propositions,  70 ;  of 
inductions,  223 

Problem  (irpo0A))pa,  that  which  is 
thrown  down),  an  assertion  put  for- 
ward for  proof  or  disproof. 

Proof,  the  assigning  a  reason  or  ar- 
gument for  the  support  of  a  given 
proposition 

Proper  names,  18 

Property  or  pro}rium>  41,  102,  109 

Propositions,  10, 16 ,  several  kinds 
of,  60 ;  affirmative  and  negative,  63 ; 
categorical,  63;  conditional,  62,  160; 
disjunctive,  62,  160 ;  essential  or  ex- 
plicative, 68;  exclusive,  exceptive, 
68  •  hypothetical,  62,  162  ;  indefinite 
or  indesignate,  65;  modal,  69,  91; 
opposition  of,  78 ;  particular,  63—^6, 
72,  79 :  pure,  69 ;  plurative,  191 ;  ir- 
regular, 67 ;  quality  and  quantity  of, 

63 

Pro«yllogi»m,  155 
Prcndoutt*  genus,  ioi 


Quantification  of  predicate,  183 
Quantity  of  propositions,  63;  qoc* 

tior.s  of  quantity,  120 
Quateroio  terminorum,  190 

Ramean  tree,  see   Tn»  »f  P*r 

pkyry 
Ratiocination,  a  name  •quivale* 

to  Syllogism  or  Deduction,  adoptei 

by  I.  S.  Mill. 
Realism,  13 
Reason  (ratio,  from  rtor,  to  think) 

a  term  of  wide  and  ambiguous  mean 

ing  ;  it  has  sometimes  been  special!] 

used  to  denote  the  minor  premise  o> 

a  syllogism. 

Reasoning,  or  discourse,  15 
Record,  language  as  instrument  of, 

Reductio  ad  absurdum  or  a* 
impossible,  an  indirect  demonstra 
tion  founded  upon  the  impossibilit3 
of  a  contradictory  supposition,  146 

Reduction  of  the  syllogistic  figures. 
145  ;  «f  hypothetical  to  categorical 
syllogisms,  163 — 5 

Relation  (relatum,  past  participle 
of  re/era,  to  bear  back),  any  con- 
nection in  thought  or  fact  betwee* 
two  things,  si 

Relative  terms,  25 

Residual  phenomena,  254 

Residues,  method  of,  252 

Rules  of  the  syllogism,  137 

Scholastic  Philosophy,  a  g» 

neral  name  for  the  systems  of  philo- 
sophy taught  during  the  middle  age} 
from  the  9th  to  the  i6th  century, 
flourishing  chiefly  in  the  i3th  and 
1 4th  centuries.  The  subject  wai 
chiefly  the  logic  of  Aristotle,  varied 
with  theology,  metaphysics,  gram- 
mar, or  rhetoric. 

Second  Intention,  m  Intention, 
Secundi  adjacentis,  of  the  se 
cond  adjacent,  an  expression  in  in* 
correct   Latin,  applied   to  a  gram- 
matical sentence  or  proposition  COP 
taining  only  two  parts,  the  subjeo 
and  verb,  without  a  distinct  copola 
Self-contradictory  terms,  143 
Semilogical  fallacies,  171 
Sentence,  grammatical.  61.  lQ 
Separable  a 


§4* 


INDEX. 


Slgniflcates  of  •  term  ure  things 

denoted  or  signified  by  it 
Similars,  substitution  of,  124,  200 
Simple,  apprehension,  n  ;  conver- 
sion, 82,  184 

Singular,  terms,  18  ;  propositions, 64 
Sophism  (cro^icr^a,  from  awpia,  wis- 
dom), a  false  argument;   the  name 
often  implies  that  a  false  argument 
is  consciously  used  for  deception. 
Sorites,  156 

Specialization  of  names,  45,  48 
Species,   in  logic,   98;   in  natural 

history,  101 
Subaltern,  propositions, 77;  genera 

and  species,  100 
Subalternans,     subaltern- 

ates,  77 

Sub  contrary  Propositions,  77 
Subject  of  a  proposition,  62,  93 
Subjective,  that  which  belongs  to 
the    thinking    subject,   the  ego,   or 
mind  engaged  in  thought ;  opposed 
to  objective,  which  see. 
Subordinate  propositions,  91 
Substance  (sub,  under ;  stans  from 
start,  to  stand),  that  which  underlies 
and  bears  phenomena  or  attributes ; 
strictly  speaking  it  is  either  mind  or 
matter,    but   it  is  more    commonly 
used  in  the  material  sense. 
Substitution  of  similars,  124,  200 
Subsumption  [sub,  under ;  sutno, 
to  take  or  put),  a  name  used  by  Sir 
W.  Hamilton  for  the  minor  premise 
of  a  syllogism,  because  it  brings  or 
nt&runtes  a  special  case  under  the 
rule  expressed  in  the  major  premise 

Subsumptipn  of  a  law  is  Mr 
Mill's  expression  for  the  third  mode 
of  explaining  a  law  by  shewing  it  to 
be  a  particular  case  of  a  more  ge- 
neral law,  268 

Sufficient  Reason,  Principle  or 
Law  of,  125 

Bui  generis,  101 

Summum  genus,  TOO 

Sumption  (sumo,  to  take),  Sir  W. 
Hamilton's  name  for  the  major  pre- 
mise of  a  syllogism. 

Supposition,  170 

Syllogism,  10,  127;  inductive.au, 

t)yrn»olical  knowledge,  57 


Syncategorematic  words,  il 

Synthesis,  205 

Synthetic   syllogism,  a  syllo 

gism  in  which  the  conclusion  stand* 

last  ;  see  A  nalytic  syllogism. 
System,  ((rv'tm^a,  from  (rwtVnm*. 

to  put  together),  a  connected  body  01 

knowledge. 

Tacit  premise,  153 

Tautologous  propositions,  69 

Tendency,  266 

Terminology,  293 

Terms,  10,  16,  17 

Tertii  adjacentts,  of  the  third 
adjacent,  an  expression  in  incorrect 
Latin,  applied  to  a  grammatical  sen- 
tence or  proposition  in  which  the 
subject,  copula  and  predicate,  are 
all  distinctly  stated. 

Theory  (9t<apia,  contemplation), 
knowledge  of  principles,  as  opposed 
to  practice;  ambiguously  used,  see 


Thesis  (0«<ri«,  from 
an  assertion  or  proposition 


o  place), 
which  u 

put  forth  to  be  proved  or  supported 

by  arguments. 
Thoughts  on  things,  the  object  o) 

logic,  10 
Totum  di  visum,  a  class  or  notion 

which  is  divided  into  parts    by  i 

difference. 
Traduction,  212 
Transfer  of  meaning  of  terms,  32 
Tree  of  Porphyry,  103 
Trilemma,    an    argument    resem- 

bling a  dilemma,  but  in  which  ther* 

are  three  alternatives. 
Truisms,  69 
Truth,  conformity  of  our  knowledg* 

with  the  things  known. 

TTltra-total  distribution,  191 
Uniformity  of  nature,  217 
Universal  propositions,  63 

66;  affirmative,  71  ;  negative,  73 
Uni  vocal  terms,  29 

Variations,   method  of,  149;   p* 

rkxlic,  250 
Verb,  88 

!    Weakened  conclusion,  140 

'    Worse  relation  (Hamilton),  19 


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